{"id":55648,"date":"2025-01-24T20:15:47","date_gmt":"2025-01-24T14:45:47","guid":{"rendered":"https:\/\/viswaguide.com\/?p=55648"},"modified":"2026-02-25T04:36:20","modified_gmt":"2026-02-24T23:06:20","slug":"ex-3-draw-the-graphs-of-5-sin-3x-2-and-4-cos-2x-1-and-find-their-domain-range-maximum-value-minimum-value-amplitude-period-and-phase-shift-using-geogebra-classic-5","status":"publish","type":"post","link":"https:\/\/viswaguide.com\/?p=55648","title":{"rendered":"i) Draw the graphs of A sin (Bx + C) and A cos (Bx + C) and find their domain, range, maximum value, minimum value, amplitude, period and phase shift using geogebra classic 5  ii) Draw the graph of sin\u207b\u00b9(x) and cos\u207b\u00b9(x) and find their domain, range, maximum value and minimum value using geogebra classic 5"},"content":{"rendered":"\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-0d4a0d23bfe2344d6a2d8bf25b18bfc7\">Aim:<\/h4>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[1.\\ \\text{To draw the graphs of A sin (Bx + C) and A cos (Bx + C) for some fixed finite}\\ \\hspace{10cm}\\\\ \\text{ real values of A, B and C.}\\hspace{10cm}\\]<script id=\"wp-hooks-js\" src=\"https:\/\/viswaguide.com\/wp-includes\/js\/dist\/hooks.min.js?ver=7496969728ca0f95732d\"><\/script>\n<script id=\"wp-i18n-js\" src=\"https:\/\/viswaguide.com\/wp-includes\/js\/dist\/i18n.min.js?ver=781d11515ad3d91786ec\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async id=\"mathjax-js\" src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[2.\\ \\text{To find their domain, range, maximum value, minimum value, amplitude,}\\ \\hspace{10cm}\\\\ \\text{ period and phase shift.}\\hspace{10cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-e354ed38548c687c69414021a6d25bf2\">Procedure<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 (by double clicking on the icon)}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To draw the graphs of A sin (Bx + C) and A cos (Bx + C) \u2192 change the x &#8211; axis \u2192}\\hspace{5cm}\\\\ \\hspace{1cm}\\ \\text{values to multiples of}\\ \\frac{\\pi}{2},\\ \\text{do the following \u2192 right click on Graphics view \u2192}\\\\ \\text{Graphics \u2192 x Axis \u2192 Distance \u2192}\\ \\frac{\\pi}{2}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{To draw graphs of A sin (Bx + C) and A cos (Bx + C) \u2192}\\ \\hspace{5cm}\\ \\\\ \\hspace{1cm}\\ \\text{press the Enter Key\u2192 the pop-up window shows \u2192 }\\\\ \\text{Create sliders for A, B,C}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To create an input box for sliders A, B and C \u2192 link with A, B and C.}\\ \\hspace{6cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\"><\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{To create an input box for Function f(x) =  \u2192 link with f(x)}\\ \\hspace{7cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To set the values A = 5, B = 3 and C = 2 by using input box}\\ \\hspace{7cm}\\\\ \\text{or using the sliders A, B and C.}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{Domain is the set of values of x for which the curve exists. By using }\\ \\hspace{7cm}\\\\ \\text{input bar to type Domain = &#8211; \u221e &lt; x &lt; \u221e and press Enter Key}\\]<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{Range is the set of values of y for which the curve exists. By using }\\ \\hspace{7cm}\\\\ \\text{input bar to type Range = &#8211; 5 \u2264 y \u2264 5 and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 9:}\\ \\text{To calculate the period of the function by using the input bar to type}\\hspace{5cm}\\\\ \\hspace{1cm}\\ \\text{Period = 2 pi\/abs(B). One cycle of f(x) = A sin (Bx + C)}\\ \\text{is given by the interval}\\\\ [ 0, \\frac{2\\pi}{|B|}]\\ \\text{and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 10:}\\ \\text{To find the maximum value in the interval}\\hspace{10cm}\\\\ \\hspace{1cm}\\  0, \\frac{2\\pi}{|B|}]\\ \\text{is by using the input bar to type M = Max{f,0,2 pi\/abs(B)}}\\\\ \\text{and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 11:}\\ \\text{To obtain the function value using the input command}\\ \\hspace{7cm}\\\\ \\text{Maximum = y(M) and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 12:}\\ \\text{To find the minimum value in the interval}\\hspace{9cm}\\\\ \\hspace{1cm}\\  [0, \\frac{2\\pi}{|B|}]\\ \\text{is by using the input bar to type}\\ \\text{m = Min(f,0,2 pi\/abs(B)}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 13:}\\ \\text{To obtain the function value using the input command}\\ \\hspace{7cm}\\\\ \\text{Minimum = y(m) and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 14:}\\ \\text{To find the Amplitude of the function by using the}\\ \\hspace{8cm}\\\\ \\hspace{1cm}\\ \\text{by using the input bar to type Amplitude = (1\/2)(Maximum-Minimum)}\\\\ \\text{and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 15:}\\ \\text{The phase shift is found by using the input bar to type}\\ \\hspace{7cm}\\\\ \\text{Phase Shift = -C\/abs(B) and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 16:}\\ \\text{To draw the graph of f(x) = 4 cos(2x &#8211; 1)}\\ \\hspace{10cm}\\\\ \\text{by using the input boxes of A, B, C and f(x)}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Output table for y = 5 sin (3x + 2) and y = 4 cos (2x &#8211; 1)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>Function<\/td><td>y = 5 sin (3x + 2)<\/td><td>y = 4 cos (2x &#8211; 1)<\/td><\/tr><tr><td>Domain<\/td><td>-\u221e &lt;= x &lt;= \u221e<\/td><td>-\u221e &lt;= x &lt;= \u221e<\/td><\/tr><tr><td>Range<\/td><td>-5 &lt;= y &lt;= 5<\/td><td>-5 &lt;= y &lt;= 5<\/td><\/tr><tr><td>Maximum value<\/td><td>(1.95 , 5)<\/td><td>(0.5 , 4)<\/td><\/tr><tr><td>Minimum  value<\/td><td>(0.9, &#8211; 5)<\/td><td>(2.07 , &#8211; 4)<\/td><\/tr><tr><td>Amplitude<\/td><td>5<\/td><td>4<\/td><\/tr><tr><td>Period<\/td><td>2.09<\/td><td>3.14<\/td><\/tr><tr><td>Phase Shift<\/td><td>&#8211; 2\/3<\/td><td>1 \/ 2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n<p><iframe width=\"747\" height=\"467\" src=\"https:\/\/www.youtube.com\/embed\/bkW-AFAfGXg\" title=\"Drawing of 5 sin(3x +2) and 4 cos (2x-1) functions using Geogebra\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen=\"\"><\/iframe><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-vivid-red-color has-text-color has-link-color wp-elements-4622daee6e2252c4ee437e3c94a26b85\">INVERSE TRIGONOMETRIC FUNCTIONS<\/h4>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-89bfda0d449bddcb20c4924e685a3000\">Aim:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{1cm}\\ \\color{green}{1.}\\ \\text{To draw the graph of sin\u207b\u00b9(x) and cos\u207b\u00b9(x)}\\ \\hspace{10cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\hspace{1cm}\\ \\color{green}{2.}\\ \\text{To find their domain, range, maximum value and minimum value}\\ \\hspace{5cm}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-caaadd60b535c837691a2eb0c3ab170e\">Procedure:<\/h5>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 1:}\\ \\text{Open Geogebra classic 5 (by double clicking on the icon)}\\ \\hspace{8cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 2:}\\ \\text{To  change the y &#8211; axis \u2192 right click on Graphics view \u2192}\\ \\hspace{10cm}\\\\ \\text{Graphics \u2192 y Axis \u2192 Distance \u2192}\\ \\frac{\\pi}{2}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 3:}\\ \\text{To draw the graph of f(x) = sin\u207b\u00b9(x) by using the input bar to type}\\ \\hspace{7cm}\\\\ \\text{Asin(x) or arcsin(x) and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 4:}\\ \\text{To set of values of x for which the graph of sin\u207b\u00b9(x) exists is called the domain.}\\ \\hspace{7cm}\\\\ \\text{by using input bar to type Domain = &#8211; 1 \u2264 x \u2264 1 and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 5:}\\ \\text{To set of values of y for which the graph of sin\u207b\u00b9(x) exists is called the range,}\\ \\hspace{7cm}\\\\ \\text{by using input bar to type Range = &#8211; pi\/2 \u2264 y \u2264 pi\/2 and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 6:}\\ \\text{To find the maximum value of the function sin\u207b\u00b9(x)}\\hspace{10cm}\\\\ \\hspace{1cm}\\  \\text{in the interval [-1,1] by using the input bar to type M = Max{f,-1,1}}\\\\ \\text{and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 7:}\\ \\text{To find the minimum value of the function sin\u207b\u00b9(x)}\\hspace{10cm}\\\\ \\hspace{1cm}\\  \\text{in the interval [-1,1] by using the input bar to type m = Min{f,-1,1}}\\\\ \\text{and press Enter Key}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 8:}\\ \\text{To create an input box for Function, link with f(x) = sin\u207b\u00b9(x) }\\ \\hspace{7cm}\\]<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\[\\color{green}{Step\\ 9:}\\ \\text{To change the function  f(x) = cos\u207b\u00b9(x) }\\ \\hspace{12cm}\\\\ \\text{by using the input box to type arccos(x) and press Enter Key}\\]<\/div>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-883bedab9864fd79dff46cd9aa765019\">Output:<\/h5>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Output for Inverse Trigonometric Function<\/p>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table class=\"has-fixed-layout\"><tbody><tr><td>Function<\/td><td>f(x) = sin\u207b\u00b9(x)<\/td><td>f(x) = cos\u207b\u00b9(x)<\/td><\/tr><tr><td>Domain<\/td><td><\/td><td><\/td><\/tr><tr><td>Range<\/td><td><\/td><td><\/td><\/tr><tr><td>Maximum Value<\/td><td><\/td><td><\/td><\/tr><tr><td>Minimum Value<\/td><td><\/td><td><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Aim: Procedure Output: Output table for y = 5 sin (3x + 2) and y = 4 cos (2x &#8211; 1) Function y = 5 sin (3x + 2) y = 4 cos (2x &#8211; 1) Domain -\u221e &lt;= x &lt;= \u221e -\u221e &lt;= x &lt;= \u221e Range -5 &lt;= y &lt;= 5 -5 &lt;= [&hellip;]<\/p>\n","protected":false},"author":187055548,"featured_media":55771,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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