{"id":11314,"date":"2021-02-24T15:14:49","date_gmt":"2021-02-24T23:14:49","guid":{"rendered":"https:\/\/www.vernier.com\/til\/?p=11314"},"modified":"2025-04-15T12:38:24","modified_gmt":"2025-04-15T19:38:24","slug":"what-functions-can-you-use-with-graphical-analysis-pro-custom-expression-calculated-columns","status":"publish","type":"post","link":"https:\/\/www.vernier.com\/til\/11314","title":{"rendered":"What functions can you use with Graphical Analysis Pro and Vernier Video Analysis &#8220;Custom Expression&#8221; calculated columns?"},"content":{"rendered":"<h3 class=\"wp-block-heading\">Expression Details<\/h3>\n<ul class=\"wp-block-list\">\n<li>An expression must be a number, a data column, an appropriately formatted function, or a combination of these items: [5, \u201cX\u201d, sin(\u201cX\u201d), 5sin(\u201cX\u201d)]<\/li>\n<li>Column names must be entered with quotes. [sin(&#8220;X&#8221;), &#8220;Y&#8221;, or abs(&#8220;Z&#8221;)]<\/li>\n<li>Supported operators are +  \u2013   *  \/   ^  (   )<\/li>\n<li>Functions must contain their arguments in parentheses. [abs(\u201cX\u201d) or sqrt(2)]<\/li>\n<li>Multiplication can be explicit or implied. [5*\u201cX\u201d, 5\u201cX\u201d, or 5(\u201cX\u201d)]<\/li>\n<li>Constants must be entered as numbers. Variable parameters (e.g., A, B, C) are not supported.<\/li>\n<li>Trigonometric functions are evaluated in radians.<\/li>\n<li>Functions can be nested as long as the proper format is used. [sqrt(abs(\u201cX\u201d))]<\/li>\n<\/ul>\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<h3 class=\"wp-block-heading\">Function Syntax<\/h3>\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<style>.kt-accordion-id11314_36c4ea-e67 .kt-accordion-inner-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:8px;}.kt-accordion-id11314_36c4ea-e67 .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;padding-top:10px;padding-right:10px;padding-bottom:10px;padding-left:10px;}.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;border-top-left-radius:2px;border-top-right-radius:2px;border-bottom-right-radius:2px;border-bottom-left-radius:2px;background:#cce8ea;font-size:18px;line-height:24px;color:#007377;padding-top:10px;padding-right:14px;padding-bottom:10px;padding-left:14px;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:before{background:#007377;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#007377;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#cce8ea;}.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67 .kt-blocks-accordion-header:focus-visible{color:#007377;background:#e6e6e4;border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion--visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#007377;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger{background:#007377;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#e6e6e4;}.kt-accordion-id11314_36c4ea-e67 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{color:#f79b2e;background:#444444;border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#f79b2e;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#f79b2e;}.kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_36c4ea-e67:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#444444;}@media all and (max-width: 1024px){.kt-accordion-id11314_36c4ea-e67 .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}@media all and (max-width: 1024px){.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;}}@media all and (max-width: 1024px){.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67 .kt-blocks-accordion-header:focus-visible{border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}}@media all and (max-width: 1024px){.kt-accordion-id11314_36c4ea-e67 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}@media all and (max-width: 767px){.kt-accordion-id11314_36c4ea-e67 .kt-accordion-inner-wrap{display:block;}.kt-accordion-id11314_36c4ea-e67 .kt-accordion-inner-wrap .kt-accordion-pane:not(:first-child){margin-top:8px;}.kt-accordion-id11314_36c4ea-e67 .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;}.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_36c4ea-e67 .kt-blocks-accordion-header:focus-visible{border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}.kt-accordion-id11314_36c4ea-e67 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_36c4ea-e67 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\">\n<div class=\"kt-accordion-wrap kt-accordion-id11314_36c4ea-e67 kt-accordion-has-19-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-xclose kt-accodion-icon-side-right\" style=\"max-width:none\">\n<div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane11314_781eae-3e8\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Analysis Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Analysis Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>analysis<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">analysis(<em>&#8220;X&#8221;,startRow,endRow<\/em>)<\/p>\n<p>analysis(&#8220;X&#8221;,2,4)<\/td>\n<td>Aggregates data from the specified rows of a column named &#8216;X&#8217; (from all data sets) into a single column of data.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>dataSets<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">dataSets(<em>&#8220;X&#8221;,startRow,endRow<\/em>)<\/p>\n<p>dataSets(&#8220;X&#8221;,2,4)<\/td>\n<td>Creates a column where the row values are the data set names from which the aggregated data was acquired.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Analysis functions aggregate data from multiple datasets into a single column.<\/strong><br \/>\u25cf <em>X<\/em>\u2014the name of the column from which data is to be copied<br \/>\u25cf <em>startRow<\/em>\u2014first row from which data is to be copied<br \/>\u25cf <em>endRow<\/em>\u2014last row from which data is to be copied<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane11314_36bb9c-af9\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Blood Pressure Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Blood Pressure Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>diastolic<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">diastolic(&#8220;Pressure&#8221;,&#8221;Time&#8221;)<\/td>\n<td>The measured arterial pressure when the heart is at rest.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>meanArterialPressure<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">meanArterialPressure(&#8220;Pressure&#8221;,&#8221;Time&#8221;)<\/td>\n<td>The pressure value at the max peak used for calculating blood pressure.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>oscillations<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">oscillations(&#8220;Pressure&#8221;,&#8221;Time&#8221;)<\/td>\n<td>Oscillations of the peaks and valleys used for calculating blood pressure.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>oscillatoryPeaks<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">oscillatoryPeaks(&#8220;Pressure&#8221;,&#8221;Time&#8221;)<\/td>\n<td>Relative maximum values from the oscillations data used to calculate systolic, diastolic, and pulse values.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>pulse<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">pulse(&#8220;Pressure&#8221;,&#8221;Time&#8221;)<\/td>\n<td>Pulse rate calculated using the blood pressure sensor inputs.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>systolic<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">systolic(&#8220;Pressure&#8221;,&#8221;Time&#8221;)<\/td>\n<td>The measured arterial pressure when the heart contracts.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>&#8220;Pressure&#8221; and &#8220;Time&#8221; are columns from data collection with a <a href=\"\/product\/blood-pressure-sensor\/\">Blood Pressure Sensor<\/a> (<nobr>BPS-BTA<\/nobr>) or <a href=\"\/product\/go-direct-blood-pressure-sensor\/\">Go Direct<sup>&reg;<\/sup> Blood Pressure Sensor<\/a> (<nobr>GDX-BP<\/nobr>).<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane11314_8993bd-d210\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Boolean Expressions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Boolean Expressions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Operator<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>AND<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"><em>&#8220;X&#8221;<\/em> AND <em>&#8220;Y&#8221;<\/em><\/td>\n<td>True (<strong>1<\/strong>) if BOTH inputs are True, otherwise False (<strong>0<\/strong>).<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">1 AND 1 = 1<br \/>1 AND 0 = 0<br \/>0 AND 1 = 0<br \/>0 AND 0 = 0<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>NOT (!)<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">! <em>&#8220;X&#8221;<\/em><\/td>\n<td>True (<strong>1<\/strong>) if the input is False. False (<strong>0<\/strong>) if the input is True.<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">! 1 = 0<br \/>! 0 = 1<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>OR<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"><em>&#8220;X&#8221;<\/em> OR <em>&#8220;Y&#8221;<\/em><\/td>\n<td>True (<strong>1<\/strong>) if AT LEAST one input is True, otherwise False (<strong>0<\/strong>).<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">1 OR 1 = 1<br \/>1 OR 0 = 1<br \/>0 OR 1 = 1<br \/>0 OR 0 = 0<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>XOR<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"><em>&#8220;X&#8221;<\/em> XOR <em>&#8220;Y&#8221;<\/em><\/td>\n<td>Exclusive OR<br \/>True (<strong>1<\/strong>) if ONLY one input is True, otherwise False (<strong>0<\/strong>).<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">1 XOR 1 = 0<br \/>1 XOR 0 = 1<br \/>0 XOR 1 = 1<br \/>0 XOR 0 = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>A Boolean expression is either True (1) or False (0) based on the operator and value of the inputs.<\/strong> When the inputs are columns, the output is a column where Boolean values are determined row-by-row.<\/p>\n<ul class=\"wp-block-list\">\n<li>Input value = <strong>False (0)<\/strong> when the input is&#8230;<br \/>\u26ac a number = 0 (must identically equal zero, not just round to zero)<\/li>\n<li>Input value = <strong>True (1)<\/strong> when the input is&#8230;<br \/>\u26ac any number \u2260 0<br \/>\u26ac Any non-numeric value (including text string = 0)<br \/>\u26ac Empty column cells<\/li>\n<\/ul>\n<p>Operators can be combined (e.g., <em>&#8220;X&#8221; AND ! &#8220;Y&#8221;<\/em>, <em>! &#8220;X&#8221; OR &#8220;Y&#8221;<\/em>, and <em>! &#8220;X&#8221; XOR ! &#8220;Y&#8221;<\/em> are valid expressions).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane11314_24e628-a911\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Calculus Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Calculus Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>firstDerivative<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">firstDerivative(<em>\u201cY\u201d,\u201cX\u201d,numberOfPoints<\/em>)<\/p>\n<p>firstDerivative(\u201cPosition\u201d,\u201cTime\u201d)<br \/>firstDerivative(\u201cPosition\u201d,\u201cTime\u201d,3)<\/td>\n<td>Finds the first derivative of data in column &#8216;Y&#8217; with respect to column &#8216;X&#8217;. &#8216;<em>numberOfPoints<\/em>&#8216; is set in Session Preferences or can be explicitly set. Default = 7<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>integral<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">integral(<em>\u201cY\u201d, \u201cX\u201d<\/em>)<\/td>\n<td>Numerical integral \u2013 the running sum of the areas of rectangles calculated using the midpoint rule. The i<sup>th<\/sup> rectangle is identified by [Y<sub>i<\/sub> \u2013 Y<sub>(i-1)<\/sub>] and [X<sub>i<\/sub> \u2013 X<sub>(i-1)<\/sub>]<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>secondDerivative<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">secondDerivative(<em>\u201cY\u201d,\u201cX\u201d,numberOfPoints<\/em>)<\/p>\n<p>secondDerivative(\u201cPosition\u201d,\u201cTime\u201d)<br \/>secondDerivative(\u201cPosition\u201d,\u201cTime\u201d,3)<\/td>\n<td>Finds the second derivative of data in column &#8216;Y&#8217; with respect to column &#8216;X&#8217;. &#8216;<em>numberOfPoints<\/em>&#8216; is set in Session Preferences or can be explicitly set. Default = 7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Derivative and Integral function parameters:<\/strong><br \/>\u25cf <em>Y<\/em>\u2014a column of data you want to differentiate or integrate<br \/>\u25cf <em>X<\/em>\u2014the independent variable column for your data; typically Time<br \/>\u25cf <em>numberOfPoints<\/em>\u2014[closest] odd integer \u2265 3 (Session Preference options: 3 ,5, 7, 9, 11, 15, or 21)<\/p>\n<p>For more information on derivative calculations, see <a href=\"\/til\/1011\/\">How do Logger <i>Pro<\/i>, Graphical Analysis, LabQuest app, and Vernier Video Analysis calculate velocity and acceleration?<\/a>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-5 kt-pane11314_5544a6-8512\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Collapse Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Collapse Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th>Function<\/th>\n<th>Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>collapse<\/strong><\/td>\n<td>collapse(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>Creates a new column equivalent to column &#8216;X&#8217; with the blank cells removed.<\/td>\n<\/tr>\n<tr>\n<td><strong>collapseIndirect<\/strong><\/td>\n<td>collapseIndirect(<em>&#8220;X&#8221;,&#8221;Y&#8221;<\/em>)<\/td>\n<td>Creates a new column containing values from only the rows in column &#8216;X&#8217; that correspond to the rows in column &#8216;Y&#8217; that are numbers (skipping rows where column &#8216;Y&#8217; has blank cells).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Collapse functions are used to remove empty cells from columns and to retain correlations between data from other columns (that do not include empty cells).<\/strong> This is helpful when wanting to use functions such as delta() and sum() with columns that contain empty cells.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-7 kt-pane11314_bca736-9b14\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Column-Fill Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Column-Fill Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>constant<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">constant(<em>constant,count<\/em>)<\/td>\n<td>This function generates a column with every cell value = &#8216;constant&#8217;.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>randInt<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">randInt(<em>min,max,count<\/em>)<\/td>\n<td>This function generates a column of random integers between the values of &#8216;min&#8217; and &#8216;max&#8217; (inclusive).<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>randReal<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">randReal(<em>min,max,count<\/em>)<\/td>\n<td>This function generates a column of random real numbers between the values of &#8216;min&#8217; and &#8216;max&#8217; (inclusive).<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>rowNumber<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">rowNumber()<\/td>\n<td>This function generates a column of values where the cell value is the row number of the cell. (This function has no arguments.)<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>step<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">step(<em>start,increment,count, firstRow,skip<\/em>)<\/td>\n<td>Generates a column having &#8216;count&#8217; rows. The first reported value is &#8216;start&#8217; and subsequent values are increased or decreased by the value of the &#8216;increment&#8217;. &#8216;firstRow&#8217; defines the row in which the first value is reported. &#8216;skip&#8217; defines is the number of rows skipped between reported values.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>stepColumnBased<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">stepColumnBased(<em>&#8220;X&#8221;,start, increment,firstRow,skip<\/em>)<\/td>\n<td>This function is similar to the step function, except output values will appear only in non-empty rows in column &#8216;X&#8217;. &#8216;firstRow&#8217; = 2 corresponds to the second non-empty row of column &#8216;X&#8217;.  &#8216;skip&#8217; = 1 will report output values in every other non-empty row of column &#8216;X&#8217;.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<ul class=\"wp-block-list\">\n<li>The data table needs to have active rows in the data set for the fill-value functions to work. These functions do not create active rows automatically.<\/li>\n<li>The number of rows in the output column is determined by the value of &#8216;<em>count<\/em>&#8216;; however, the value is limited by the number of active rows in the dataset.<\/li>\n<li>When &#8216;<em>count<\/em>&#8216; is a column (e.g., &#8216;X&#8217;), the value of &#8216;<em>count<\/em>&#8216; is number of rows in column &#8216;X&#8217;.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-6 kt-pane11314_7e33d6-ce13\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Column-Manipulation Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Column-Manipulation Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>abs<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">abs(<em>arg1<\/em>)<\/td>\n<td>absolute value (|x|)<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>delta<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">delta(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>The difference between consecutive values from column &#8216;X&#8217;. (The i<sup>th<\/sup> value of the output is i<sup>th<\/sup> value of &#8216;X&#8217; minus the (i-1)<sup>th<\/sup> value of &#8216;X&#8217;.) The output will have an empty first row.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>interpolate<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">interpolate(<em>&#8220;Y&#8221;,&#8221;X&#8221;<\/em>)<\/td>\n<td>This function generates a column where missing values in the &#8216;Y&#8217; column are filled in using linear interpolation. Column &#8216;X&#8217; is the independent variable, typically Time.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>rms<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">rms(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>Cumulative Root Mean Square of the values in column &#8216;X&#8217; up to the current row. The output value reported for row 3 is sqrt((X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup>+X<sub>3<\/sub><sup>2<\/sup>)\/3))<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>subset<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">subset(<em>&#8220;X&#8221;,start,step<\/em>)<\/td>\n<td>Returns a column of data extracted from column &#8216;X&#8217; starting with the row numbered &#8216;start&#8217;, incremented by &#8216;step&#8217; rows. Rows in column &#8216;X&#8217; that are skipped are blank in the output column.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>sum<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sum(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>The sum of the values in column &#8216;X&#8217; up to the current row. The output value reported for row 3 is the sum of the column &#8216;X&#8217; values from rows 1, 2 and 3.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>value<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">value(<em>offset,&#8221;X&#8221;<\/em>)<\/td>\n<td>Creates a new column based on column &#8216;X&#8217; by extracting values from column &#8216;X&#8217; that are &#8216;offset&#8217; rows from the current row. <br \/><em>offset<\/em> = -2 has column &#8216;X&#8217; row 1 copied to output row 3 with the first two rows of the output blank.<br \/><em>offset<\/em> = 2 has column &#8216;X&#8217; row 3 copied to output row 1 with the last two rows of the output blank.<br \/><em>offset<\/em> = 0 will have an output that duplicates column &#8216;X&#8217;.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Function parameters:<\/strong><br \/>\u25cf <em>X<\/em> and <em>Y<\/em>\u2014are columns of data<br \/>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<br \/>\u25cf <em>offset<\/em>, <em>start<\/em>, and <em>step<\/em>\u2014are integers<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-8 kt-pane11314_46dc56-0d15\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Digital Filter Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Digital Filter Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>bandPassFilter<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">bandPassFilter(<em>\u201cY\u201d<\/em>,<em>\u201cX\u201d<\/em>,<em>bandPassRipple<\/em>,<em> lowCutoff<\/em>,<em>highCutoff<\/em>)<\/p>\n<p>bandPassFilter(\u201cSignal\u201d,\u201cTime\u201d,0.5,1, 50)<\/td>\n<td>Filter data that have unwanted FFT frequencies outside two &#8216;cutoff&#8217; values. For EKG\/EMG data, filter frequencies below 1 Hz to remove noise from arm or leg movements, and filter frequencies above 50 hz to remove noise from a US power supply.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>bandStopFilter<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">bandStopFilter(<em>\u201cY\u201d<\/em>,<em>\u201cX\u201d<\/em>,<em>bandPassRipple<\/em>,<em> lowCutoff<\/em>,<em>highCutoff<\/em>)<\/p>\n<p>bandStopFilter(\u201cPotential\u201d,\u201cTime\u201d,0.5,50,70)<\/td>\n<td>Filter data that have unwanted FFT frequencies between two &#8216;cutoff&#8217; values. For voltage data, use a 50 to 70 Hz band stop filter to remove noise from a US power supply.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>highPassFilter<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">highPassFilter(<em>\u201cY\u201d<\/em>,<em>\u201cX\u201d<\/em>,<em>bandPassRipple<\/em>,<em>cutoff<\/em>)<\/p>\n<p>highPassFilter(\u201cSignal\u201d,\u201cTime\u201d,0,1)<\/td>\n<td>Filter data that have unwanted FFT frequencies below the &#8216;cutoff&#8217; value. For EMG data, use a 1 Hz high pass filter to remove noise from muscle movements such as a twitch.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>lowPassFilter<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">lowPassFilter(<em>\u201cY\u201d<\/em>,<em>\u201cX\u201d<\/em>,<em>bandPassRipple,cutoff<\/em>)<\/p>\n<p>lowPassFilter(\u201cSignal\u201d,\u201cTime\u201d,0,50)<\/td>\n<td>Filter data that have unwanted FFT frequencies above the &#8216;cutoff&#8217; value. For EKG data, use a 50 Hz low pass filter to remove noise from a power supply affecting your data.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>timeDecayFilter<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">timeDecayFilter(<em>\u201cY\u201d<\/em>,<em>\u201cX\u201d<\/em>,<em>timeDecay<\/em>)<\/td>\n<td>Use this function to apply a time decay to the data.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Digital Filter functions are designed to work with analog sensors and\/or truly analog signals.<\/strong> Signals or sensors that perform digital signal processing may not work well with these features.<\/p>\n<ul class=\"wp-block-list\">\n<li><em>Y<\/em>\u2014the column of data to which the filter is being applied<\/li>\n<li><em>X<\/em>\u2014the independent variable column for your data; typically Time<\/li>\n<li><em>bandPassRipple<\/em>\u2014This value is the percentage of pass-band<br \/>\u26ac Low Pass and High Pass filters are typically 0, which applies a Butterworth filter<br \/>\u26ac Band Stop and Band Pass filters are typically 0.5, which applies a Chebyshev filter<br \/>\u26ac To mimic an analog filter circuit, set the bandPassRipple to 0<br \/>\u26ac In most cases, a bandPassRipple set to 0.1 will give the best results<\/li>\n<li><em>cutoff<\/em>, <em>lowCutoff<\/em>, <em>highCutoff<\/em>\u2014the FFT frequency cutoff value used for the filter; must be a number<\/li>\n<li><em>timeDecay<\/em>\u2014time decay constant, typically in seconds<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-9 kt-pane11314_0b64a7-3016\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Energy Sensor Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Energy Sensor Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>energy<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">energy(&#8220;Potential&#8221;,&#8221;Current&#8221;)<\/td>\n<td>Calculates Energy in Joules (J)<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>power<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">power(&#8220;Potential&#8221;,&#8221;Current&#8221;)<\/td>\n<td>Calculates Power in milliwatts (mW)<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>resistance<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">resistance(&#8220;Potential&#8221;,&#8221;Current&#8221;)<\/td>\n<td>Calculates Resistance in ohms (\u03a9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>&#8220;Potential&#8221; (measured in V) and &#8220;Current&#8221; (measured in mA) are columns from data collection with a <a href=\"\/product\/vernier-energy-sensor\/\">Vernier Energy Sensor<\/a> (<nobr>VES-BTA<\/nobr>) or <a href=\"\/product\/go-direct-energy-sensor\/\">Go Direct<sup>&reg;<\/sup> Energy Sensor<\/a> (<nobr>GDX-NRG<\/nobr>).<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-10 kt-pane11314_7afa5c-9d17\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Exponential and Logarithmic Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Exponential and Logarithmic Functions<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>exp<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">exp(arg1)<\/td>\n<td>Natural (base-e) exponential function (e<sup>x<\/sup>)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">exp(2) \u2248 7.389<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>exp2<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">exp2(arg1)<\/td>\n<td>base-2 exponential function (2<sup>x<\/sup>)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">exp2(2) = 4&nbsp;<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>expm1<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">expm1(arg1)<\/td>\n<td>e<sup>x<\/sup>\u20131 or exp(x)\u20131<br \/>Greater accuracy for &#8216;x&#8217; values close to 0.<br \/>Inverse of log1p(x).<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">expm1(0.005)<br \/>\u2248&nbsp;0.005012521<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>ln<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">ln(arg1)<\/td>\n<td>Natural or base-e logarithmic function&nbsp;<br \/>(ln x or log<sub>e<\/sub> x)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">ln(2.719) \u2248 1<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>log<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">log(arg1)<\/td>\n<td>common or base-10 logarithmic function <br \/>(log x or log<sub>10<\/sub>x)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">log(1000) = 3<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>log1p<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">log1p(arg1)<\/td>\n<td>ln(1+x)<br \/>Greater accuracy for &#8216;x&#8217; values close to 0. <br \/>Inverse of expm1(x)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">log1p(0.005012512)<br \/>\u2248&nbsp;0.005<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>log2<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">log2(arg1)<\/td>\n<td>base-2 logarithmic function (log<sub>2<\/sub>x)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">log2(8) = 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-11 kt-pane11314_018d19-4118\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Modulo (Integer Remainder) Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Modulo (Integer Remainder) Functions<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>mod<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">mod(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>Modulo &#8211; integer remainder of X\/Y<br \/>mod(x,y) = x &#8211; y*trunc(x\/y)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">mod(5,4) = 1<br \/>mod(6,4) = 2<br \/>mod(7,4) = 3<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>remainder<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">remainder(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>ISEE &#8211; integer remainder of X\/Y<br \/>remainder(x,y) = x &#8211; y*round(x\/y)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">remainder(5,4) = 1<br \/>remainder(6,4) = -2<br \/>remainder(7,4) = -1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-12 kt-pane11314_1a9fd5-4419\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Photogate and Projectile Launcher Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Photogate and Projectile Launcher Functions<\/h3>\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<style>.kt-accordion-id11314_4874e9-ab .kt-accordion-inner-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:8px;}.kt-accordion-id11314_4874e9-ab .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;padding-top:10px;padding-right:10px;padding-bottom:10px;padding-left:10px;}.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid 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.kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion--visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#007377;}.kt-accordion-id11314_4874e9-ab:not( 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body:not(.hide-focus-outline) .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#e6e6e4;}.kt-accordion-id11314_4874e9-ab .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{color:#f79b2e;background:#444444;border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}.kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#f79b2e;}.kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#f79b2e;}.kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_4874e9-ab:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#444444;}@media all and (max-width: 1024px){.kt-accordion-id11314_4874e9-ab .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}@media all and (max-width: 1024px){.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;}}@media all and (max-width: 1024px){.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_4874e9-ab .kt-blocks-accordion-header:focus-visible{border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}}@media all and (max-width: 1024px){.kt-accordion-id11314_4874e9-ab .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}@media all and (max-width: 767px){.kt-accordion-id11314_4874e9-ab .kt-accordion-inner-wrap{display:block;}.kt-accordion-id11314_4874e9-ab .kt-accordion-inner-wrap .kt-accordion-pane:not(:first-child){margin-top:8px;}.kt-accordion-id11314_4874e9-ab .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;}.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_4874e9-ab .kt-blocks-accordion-header:focus-visible{border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}.kt-accordion-id11314_4874e9-ab .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_4874e9-ab > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\">\n<div class=\"kt-accordion-wrap kt-accordion-id11314_4874e9-ab kt-accordion-has-4-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-xclose kt-accodion-icon-side-right\" style=\"max-width:none\">\n<div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane11314_21715d-a8\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Projectile Launcher \u2014<\/strong> Launch Speed and Time of Flight<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Projectile Launcher Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Gate Time<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEPLGateTime(<em>&#8220;Time&#8221;,&#8221;Gate State&#8221;,&#8221;Gate State&#8221;<\/em>)<\/td>\n<td>Calculates the time between the first blocked event and the next unblocked event.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Launch Speed<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEVelocity(<em>&#8220;X&#8221;,distance<\/em>)<\/p>\n<p>DEVelocity(&#8220;Pulse Time&#8221;,0.05)<br \/>DEVelocity(&#8220;Gate Time&#8221;,0.017247)<\/td>\n<td>Calculates the Launch Speed of the projectile using as &#8216;distance&#8217; either the projectile launcher&#8217;s photogate separation and the pulse time, or the projectile&#8217;s diameter and the gate time.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Pulse Time<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEPLPulseTime(&#8220;Time&#8221;,&#8221;Gate State&#8221;,&#8221;Gate State&#8221;)<\/td>\n<td>Calculates the time between the first two blocked events. <\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Time of Flight<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEPLTimeOfFlight(&#8220;Time&#8221;,&#8221;Gate State&#8221;,&#8221;Gate State&#8221;)<\/td>\n<td>Calculates the time between the first blocked event and the third blocked event.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>The inputs for these calculations are the Gate State and Time columns from <a href=\"\/product\/vernier-projectile-launcher\/\">Vernier Projectile Launcher<\/a> (<nobr>VPL<\/nobr>) or <a href=\"\/product\/go-direct-projectile-launcher\/\">Go Direct<sup>&reg;<\/sup> Projectile Launcher<\/a> (<nobr>GDX-PL<\/nobr>).<\/strong> The projectile launcher&#8217;s photogates and optional <a href=\"\/product\/time-of-flight-pad\/\">Time of Flight Pad<\/a> (<nobr>TOF-VPL<\/nobr>) are the equivalent of two (or three) photogates daisy-chained together.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane11314_6324f2-7b\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Single Photogate \u2014<\/strong> Linear Motion and Angular Motion (Motion Timing)<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Single Photogate<\/h3>\n<p>Linear and Angular Motion<\/p>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>firstDerivative TimeShift<\/strong><br \/>(Velocity)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">firstDerivativeTimeShift(&#8220;Distance&#8221;,&#8221;Time&#8221;)<\/td>\n<td>Used to find Velocity from Distance and Time data.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>secondDerivative TimeShift<\/strong><br \/>(Acceleration)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">secondDerivativeTimeShift(&#8220;Distance&#8221;,<br \/>&#8220;Time&#8221;)<\/td>\n<td>Used to find Acceleration from Distance and Time data.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>stepColumnBased<\/strong><br \/>(Distance)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">stepColumnBased(<em>&#8220;X&#8221;,start,increment,<br \/>firstRow,skip<\/em>)<\/p>\n<p><em>Linear Motion\u2014Picket Fence<\/em><br \/>(&#8220;Gate State&#8221;,0,0.05,1,1)<\/p>\n<p><em>Linear Motion\u2014Cart Picket Fence<\/em><br \/>(&#8220;Gate State&#8221;,0,0.01,1,1)<\/p>\n<p><em>Angular Motion\u201410-spoke pulley<\/em><br \/>(&#8220;Gate State&#8221;,0,0.6283,1,1)<\/td>\n<td>Used to generate Distance data from Gate State data.<\/p>\n<p><em>X<\/em>\u2014Gate State column<br \/><em>start<\/em>\u2014initial distance (= 0)<br \/><em>increment<\/em>\u2014distance traveled between blocked events<br \/><em>firstRow<\/em>\u2014which non-empty row in Gate State column to start from<br \/><em>skip<\/em>\u2014number of non-empty Gate State rows to skip for next value<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Gate State, Distance, and Time columns are from data collection with wired <a href=\"\/product\/photogate\/\">Photogate<\/a> (<nobr>VPG-BTD<\/nobr>) or from data collection with <a href=\"\/product\/go-direct-photogate\/\">Go Direct<sup>&reg;<\/sup> Photogate<\/a> (<nobr>GDX-VPG<\/nobr>) setup to use Gate State sensor channels.<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane11314_88bc72-77\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Single Photogate \u2014<\/strong> Speed Through Gate, Timing, Pendulum Period<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Single Photogate Functions<\/h3>\n<p>Speed Through Gate, Timing, Pendulum Timing<\/p>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Blocked to Blocked Times<\/strong><br \/>(Pulse Time)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEBlockToBlock(&#8220;Time&#8221;,&#8221;Gate State&#8221;,&#8221;Gate State&#8221;)<\/td>\n<td>Calculates the time between successive blocked events.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Blocked to Unblocked Times<\/strong><br \/>(Gate Time)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEBlockToUnblock(&#8220;Time&#8221;,&#8221;Gate State&#8221;,&#8221;Gate State&#8221;)<\/td>\n<td>Calculates the time between a blocked event and the next unblocked event.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Pendulum Period<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEPendulumPeriod(&#8220;Time&#8221;,&#8221;Gate State&#8221;,&#8221;Gate State&#8221;)<\/td>\n<td>Calculates the time between every second blocked event (after the first blocked event).<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Speed Through Gate<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEVelocity(<em>&#8220;X&#8221;,distance<\/em>)<\/p>\n<p>DEVelocity(&#8220;Gate Time&#8221;,0.05)<br \/>DEVelocity(&#8220;Pulse Time&#8221;,0.02)<\/td>\n<td>Calculates the speed by dividing the blocking object&#8217;s width (&#8216;distance&#8217;) by the Gate Time. If using Pulse Time, &#8216;distance&#8217; is how far the object travels between blocked events.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Gate State and Time columns are from data collection with wired <a href=\"\/product\/photogate\/\">Photogate<\/a> (<nobr>VPG-BTD<\/nobr>) or from data collection with <a href=\"\/product\/go-direct-photogate\/\">Go Direct<sup>&reg;<\/sup> Photogate<\/a> (<nobr>GDX-VPG<\/nobr>) setup to use Gate State sensor channels.<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane11314_5be967-53\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Two Photogates<strong> \u2014<\/strong><\/strong> Speed Between Gates, Timing<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Two Photogate Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Blocked to Blocked Time<\/strong><br \/>(Pulse Time)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEBlockToBlock(&#8220;Time&#8221;,&#8221;Gate State 1&#8243;,&#8221;Gate State 2&#8243;)<\/td>\n<td>Calculates the time between a blocked event on Gate 1 and the next blocked event on Gate 2. (Gate 1 must be blocked before Gate 2).<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>Speed Between Gates<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">DEVelocity(<em>&#8220;X&#8221;,distance<\/em>)<\/p>\n<p>DEVelocity(&#8220;Pulse Time&#8221;,0.10)<\/td>\n<td>Calculates the speed by dividing the &#8216;distance&#8217; between the photogates by the Pulse Time.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Gate State and Time columns are from data collection with wired <a href=\"\/product\/photogate\/\">Photogate<\/a> (<nobr>VPG-BTD<\/nobr>) or from data collection with <a href=\"\/product\/go-direct-photogate\/\">Go Direct<sup>&reg;<\/sup> Photogate<\/a> (<nobr>GDX-VPG<\/nobr>) setup to use Gate State sensor channels.<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<p><strong>Use these functions to calculate typical photogate measurements when collecting time-based data.<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-13 kt-pane11314_600d4f-1d20\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Power Functions (x<sup>n<\/sup>)<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Power Functions (x<sup>n<\/sup>)<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>cbrt<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">cbrt(<em>arg1<\/em>)<\/td>\n<td>cube root<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">cbrt(27) = 3<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>pow<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">pow(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>power (x<sup>y<\/sup>)<br \/>x = <em>arg1<\/em> and y = <em>arg2<\/em><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">pow(5,3) = 125<br \/>power(3,5) = 243<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>sqrt<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sqrt(<em>arg1<\/em>)<\/td>\n<td>square root<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sqrt(81) = 9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-14 kt-pane11314_1efc56-e521\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Rate and Beats Per Minute Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Rate and Beats Per Minute Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>rate<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">rate(<em>&#8220;Y&#8221;,&#8221;X&#8221;,t,m1,m2,n,dt<\/em>)<\/p>\n<p>rate(&#8220;Signal&#8221;,&#8221;Time&#8221;,15,0.4,0.6,0,5)<\/td>\n<td>The rate of column &#8216;Y&#8217; with respect to column &#8216;X&#8217;, where t is the time interval measured, &#8216;m1&#8217; is min percentage threshold, &#8216;m2&#8217; is max percentage threshold, &#8216;n&#8217; is noise threshold, and &#8216;dt&#8217; is the offset to start of the next range.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>beatsPerMinute<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">beatsPerMinute(<em>&#8220;Y&#8221;,&#8221;X&#8221;,t,m1,m2,n,dt<\/em>)<\/td>\n<td>This function is similar to the rate function except that the interval (&#8216;t&#8217;) is in seconds and the output values are in minutes.<br \/>If column &#8216;X&#8217; is in seconds, then beatsPerMinute(&#8220;Y&#8221;,&#8221;X&#8221;) = 60*rate(&#8220;Y&#8221;,&#8221;X&#8221;)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>Y<\/em>\u2014a column of data for which you want to determine the rate of oscillation<br \/>\u25cf <em>X<\/em>\u2014the independent variable column for your data; typically Time<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-15 kt-pane11314_90c633-2722\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Rounding Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Rounding Functions<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>ceiling<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">ceiling(<em>arg1<\/em>)<\/td>\n<td>Nearest integer greater than a given number.<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">ceiling(3.5) = 4<br \/>ceiling(-3.5) = -3<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>floor<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">floor(<em>arg1<\/em>)<\/td>\n<td>Nearest integer less than a given number.<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">floor(3.5) = 3<br \/>floor(-3.5) = -4<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>integer<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">integer(<em>arg1<\/em>)<\/td>\n<td>Integer part of a given number.<br \/>interger(<em>arg1<\/em>) = trunc(<em>arg1<\/em>)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">interger(3.5) = 3<br \/>interger(-3.5) = -3<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>round<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">round(<em>arg1<\/em>)<\/td>\n<td>Rounds to the nearest integer. <br \/>When the decimal value of &#8216;arg1&#8217; is exactly 0.5, values are rounded up if &#8216;arg1&#8217;&gt;0 and rounded down if &#8216;arg1&#8242;&lt;0.<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">round(3.5) = 4<br \/>round(-3.5) = -4<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>trunc<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">trunc(<em>arg1<\/em>)<\/td>\n<td>Truncate &#8211; Integer part of a given number.<br \/>trunc(<em>arg1<\/em>) = interger(<em>arg1<\/em>)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">trunc(3.5) = 3<br \/>trunc(-3.5) = -3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-16 kt-pane11314_d89a14-9223\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Smoothing Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Smoothing Functions<\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>smoothAve<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">smoothAve(<em>&#8220;Y&#8221;<\/em>)<\/td>\n<td>This function returns a column of moving averages of the values in column &#8216;Y&#8217;. &#8216;numberOfPoints&#8217; is set in Session Preferences. Default = 7<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>smoothSG<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">smoothSG(<em>&#8220;Y&#8221;,&#8221;X&#8221;,numberOfPoints<\/em>)<\/p>\n<p>smoothSG(\u201cPosition\u201d,\u201cTime\u201d)<br \/>smoothSG(\u201cPosition\u201d,\u201cTime\u201d,3)<\/td>\n<td>Savitsky-Goley smoothing fits a polynomial to a number of points around each point and computes the value of the polynomial at that point. &#8216;numberOfPoints&#8217; is set in Session Preferences or can be explicitly set. Default = 7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p><strong>Smoothing functions.<\/strong><br \/>\u25cf <em>Y<\/em>\u2014is the columns of numbers you want to smooth<br \/>\u25cf <em>X<\/em>\u2014the independent variable column for your data; typically Time<br \/>\u25cf <em>numberOfPoints<\/em>\u2014[closest] odd integer \u2265 3 (Session Preferences: 3 ,5, 7, 9, 11, 15, or 21.)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-17 kt-pane11314_1fa1b3-9024\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Statistical Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Statistical Functions<\/h3>\n<figure class=\"wp-block-table is-style-regular\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>max<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">max(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>Reports the largest number in column &#8216;X&#8217;.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>max2<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">max2(<em>&#8220;X&#8221;,&#8221;Y&#8221;<\/em>)<br \/>max2(<em>&#8220;X&#8221;, 5<\/em>)<\/td>\n<td>Compares the values in column &#8216;X&#8217;, row by row, with values in column &#8216;Y&#8217; (or some constant) and reports the larger of the two numbers for the corresponding row in the output column.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>mean<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">mean(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>Arithmetic mean of the numbers in column &#8216;X&#8217;.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>median<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">median(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>The median (middle) value of the ranked (ordered) values in column &#8216;X&#8217;. Column &#8216;X&#8217; does not need to be sorted.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>min<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">min(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>Reports the smallest number in column &#8216;X&#8217;.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>min2<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">min2(<em>&#8220;X&#8221;,&#8221;Y&#8221;<\/em>)<br \/>min2(<em>&#8220;X&#8221;,5<\/em>)<\/td>\n<td>Compares the values in column &#8216;X&#8217;, row by row, with values in column &#8216;Y&#8217; (or some constant) and reports the smaller of the two numbers for the corresponding row in the output column.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>numRows<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">numRows(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>This outputs the number of rows in column &#8216;X&#8217;.<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>rms<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">rms(<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>Cumulative Root Mean Square of the values in column &#8216;X&#8217; up to the current row. The output value reported for row 3 is sqrt((X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup>+X<sub>3<\/sub><sup>2<\/sup>)\/3))<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>stddev<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">stddev (<em>&#8220;X&#8221;<\/em>)<\/td>\n<td>The standard deviation of the numbers in a column &#8216;X&#8217;.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>X<\/em> and <em>Y<\/em>\u2014are columns of numbers<br \/>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-18 kt-pane11314_8148c1-fe25\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Trigonometric Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Trigonometric Functions<\/h3>\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<style>.kt-accordion-id11314_d65e65-63 .kt-accordion-inner-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:8px;}.kt-accordion-id11314_d65e65-63 .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;padding-top:10px;padding-right:10px;padding-bottom:10px;padding-left:10px;}.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;border-top-left-radius:2px;border-top-right-radius:2px;border-bottom-right-radius:2px;border-bottom-left-radius:2px;background:#cce8ea;font-size:18px;line-height:24px;color:#007377;padding-top:10px;padding-right:14px;padding-bottom:10px;padding-left:14px;}.kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:before{background:#007377;}.kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( 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.kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion--visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#007377;}.kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger{background:#007377;}.kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#e6e6e4;}.kt-accordion-id11314_d65e65-63 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{color:#f79b2e;background:#444444;border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}.kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#f79b2e;}.kt-accordion-id11314_d65e65-63:not( .kt-accodion-icon-style-basic ):not( 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.wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;}}@media all and (max-width: 1024px){.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63 .kt-blocks-accordion-header:focus-visible{border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}}@media all and (max-width: 1024px){.kt-accordion-id11314_d65e65-63 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}@media all and (max-width: 767px){.kt-accordion-id11314_d65e65-63 .kt-accordion-inner-wrap{display:block;}.kt-accordion-id11314_d65e65-63 .kt-accordion-inner-wrap .kt-accordion-pane:not(:first-child){margin-top:8px;}.kt-accordion-id11314_d65e65-63 .kt-accordion-panel-inner{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top:1px solid #cdcdc9;border-right:1px solid #cdcdc9;border-bottom:1px solid #cdcdc9;border-left:1px solid #cdcdc9;}.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id11314_d65e65-63 .kt-blocks-accordion-header:focus-visible{border-top:1px solid #66bac0;border-right:1px solid #66bac0;border-bottom:1px solid #66bac0;border-left:1px solid #66bac0;}.kt-accordion-id11314_d65e65-63 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id11314_d65e65-63 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{border-top:1px solid #f79b2e;border-right:1px solid #f79b2e;border-bottom:1px solid #f79b2e;border-left:1px solid #f79b2e;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\">\n<div class=\"kt-accordion-wrap kt-accordion-id11314_d65e65-63 kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-xclose kt-accodion-icon-side-right\" style=\"max-width:none\">\n<div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane11314_ded265-ef\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Hyperbolic Trigonometric Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Hyperbolic Trigonometric Functions<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>acosh<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">acosh(<em>arg1<\/em>)<\/td>\n<td>inverse hyperbolic cosine<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">acosh(2)\u22481.317<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>asinh<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">asinh(<em>arg1<\/em>)<\/td>\n<td>inverse hyperbolic sine<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">asinh(1)\u22480.4812<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>atanh<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">atanh(<em>arg1<\/em>)<\/td>\n<td>inverse hyperbolic tangent<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">atanh(0.5)\u22480.5493<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>cosh<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">cosh(<em>arg1<\/em>)<\/td>\n<td>hyperbolic cosine<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">cosh(1.317)\u22482<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>sinh<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sinh(<em>arg1<\/em>)<\/td>\n<td>hyperbolic sine<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sinh(0.4812)\u22481<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>tanh<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">tanh(<em>arg1<\/em>)<\/td>\n<td>hyperbolic tangent<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">tanh(0.5493)\u22480.5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane11314_c715a5-e9\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Standard Trigonometric Function<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Standard Trigonometric Functions<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>acos<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">acos(<em>arg1<\/em>)<\/td>\n<td>arccosine <em>or<\/em> inverse cosine (output in radians)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">acos(0.5)\u22481.047<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>asin<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">asin(<em>arg1<\/em>)<\/td>\n<td>arcsine <em>or<\/em> inverse sine (output in radians)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">asin(0.5)\u22480.5236<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>atan<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">atan(<em>arg1<\/em>)<\/td>\n<td>arctangent <em>or<\/em> inverse tangent (output in radians)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">atan(1)\u22480.785<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>atan2<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">atan2(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>2-argument arctangent&nbsp;\u2014 The angle (in radians) between the x-axis and a line connecting the origin and the point (x,y)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">atan2(4,3)\u22480.927<br \/>atan2(3,4)\u22480.644<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>cos<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">cos(<em>arg1<\/em>)<\/td>\n<td>cosine (&#8216;arg1&#8217; in radians)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">cos(1.407)\u22480.5<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>sin<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sin(<em>arg1<\/em>)<\/td>\n<td>sine (&#8216;arg1&#8217; in radians)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">sin(0.5236)\u22480.5<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>tan<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">tan(<em>arg1<\/em>)<\/td>\n<td>tangent (&#8216;arg1&#8217; in radians)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">tan(0.785398)\u22481<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<p>\u25cf Trigonometric functions are evaluated in radians.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-19 kt-pane11314_8a7da7-2126\">\n<div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\" type=\"button\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"><strong>Miscellaneous Functions<\/strong><\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div>\n<div class=\"kt-accordion-panel kt-accordion-panel-hidden\">\n<div class=\"kt-accordion-panel-inner\">\n<h3 class=\"wp-block-heading\">Miscellaneous Functions<\/h3>\n<figure class=\"wp-block-table inline\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">Function<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Syntax<\/th>\n<th>Description<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">Examples<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>copysign<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">copysign(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>Changes the sign of a number to match the sign of another number<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">copysign(-5,1)=5<br \/>copysign(5,-2)=-5<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>dim<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">dim(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>Calculates the difference between two numbers and reports the value if the difference is \u2265 0; otherwise reports 0.<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">dim(10,8) = 2<br \/>dim(10,9.9) = 0.1<br \/>dim(8,10) = 0<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>erf<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">erf(<em>arg1<\/em>)<\/td>\n<td>error function or Gauss error function<br \/><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"68\" class=\"wp-image-11339\" style=\"width: 150px;\" src=\"https:\/\/www.vernier.com\/til\/wp-content\/uploads\/sites\/2\/2021\/02\/error-function.png\" alt=\"\"><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">erf(.25) \u2248 0.276<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>erfc<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">erfc(<em>arg1<\/em>)<\/td>\n<td>Complementary error function<br \/>erfc(x) = 1 &#8211; erf(x)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">erfc(.25) \u2248 0.724<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>hypot<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">hypot(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>Hypotenuse<br \/>hypot(x,y) = sqrt(x<sup>2<\/sup> + y<sup>2<\/sup>)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">hypot(5,12) = 13<br \/>hypot(4,3) = 5<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>logb<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">logb(<em>arg1<\/em>)<\/td>\n<td>floating-point base logarithmic function, logb(<em>x<\/em>), returns the unbiased exponent value of &#8216;<em>x<\/em>&#8216; as a signed integer represented as a floating-point value.<br \/>logb(arg1) = floor(log2(abs(arg1)))<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">logb(10) = 3<br \/>logb(-1.5) = 0<br \/>logb(0.1) = -4<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>nextafter<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">nextafter(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td><a href=\"https:\/\/pubs.opengroup.org\/onlinepubs\/009695399\/functions\/nextafter.html\">Computes next representable float<\/a> after X in the direction of Y<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">nextafter(1\/0,1)=infinity<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>PolarRadius<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">PolarRadius(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>Finds r when coverting cartesian to polar coordinates (x,y) \u2192 (r,\u03b8)<br \/>r = sqrt(x<sup>2<\/sup> + y<sup>2<\/sup>) = hypot(x,y)<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">PolarRadius(1,1)\u22481.414<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"><strong>PolarTheta<\/strong><\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">PolarTheta(<em>arg1<\/em>,<em>arg2<\/em>)<\/td>\n<td>Finds \u03b8 when coverting cartesian to polar coordinates (x,y) \u2192 (r,\u03b8)<br \/>\u03b8 = atan(y\/x); 0 \u2264 \u03b8 &lt; 2\u03c0 radians<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">PolarTheta(1,1)\u22480.785<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p>\u25cf <em>arg1<\/em>\u2014can be a number, an expression that resolves to a number, or a column of numbers (<em>&#8220;X&#8221;<\/em>).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<h3 class=\"wp-block-heading\">Related Links<\/h3>\n<ul class=\"wp-block-list\">\n<li><a href=\"\/til\/3475\/\">Graphical Analysis Troubleshooting and FAQs<\/a><\/li>\n<li><a href=\"\/til\/10230\/\">Graphical Analysis Pro Troubleshooting and FAQs<\/a><\/li>\n<li><a href=\"\/til\/7037\/\">Vernier Video Analysis Troubleshooting and FAQs<\/a><\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Expression Details Function Syntax Related Links<\/p>\n","protected":false},"author":1698,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[],"tags":[],"class_list":["post-11314","post","type-post","status-publish","format-standard","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts\/11314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/users\/1698"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/comments?post=11314"}],"version-history":[{"count":0,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/posts\/11314\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/media?parent=11314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/categories?post=11314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vernier.com\/til\/wp-json\/wp\/v2\/tags?post=11314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}