The following diagrams show how to determine the transformation of a Trigonometric Graph from its equation. Scroll down the page for more examples and solutions.<\/p>\n\n\n\n The amplitude of a trigonometric function is the maximum displacement on the graph of that function.<\/p>\n\n\n\n In the case of sin and cos functions, this value is the leading coefficient of the function.<\/p>\n\n\n\n If y = A sin x, then the amplitude is |A|.<\/p>\n\n\n\n In the case of tan, cot, sec, and csc, the amplitude would be infinitely large regardless of the value of A. However, for a limited domain, the value of A would determine the maximum height of these functions.<\/p>\n\n\n\n The period of a function is the displacement of x at which the graph of the function begins to repeat.<\/p>\n\n\n\n Consider y = sin x<\/p>\n\n\n\n The value x = 2\u03c0 is the point at which the graph begins to repeat that of the first quadrant. The coefficient of x is the constant that determine the period.<\/p>\n\n\n\n The general form is y = A sin Bx where |A| is the amplitude and B determines the period.<\/p>\n\n\n\n For the functions sin, cos, sec and csc, the period is found by P = 2\u03c0\/B<\/p>\n\n\n\n Example:<\/strong> Solution:<\/strong> The general form for the equation of the sine trigonometric function is The graph y = sin x may be moved or shifted to the left or to the right. If C is positive, the shift is to the left; if C is negative the shift is to the right.<\/p>\n\n\n\n A similar general form can be obtained for the other trigonometric functions.<\/p>\n\n\n\n Example:<\/strong> Solution:<\/strong> The amplitude is 2, the period is \u03c0 and the phase shift is \u03c0\/4 units to the left.<\/p>\n\n\n\n Basic Sine Function<\/strong> In these lessons, we will learn how Trigonometric Graphs can be transformed the amplitude and vertical shift of Trigonometric Graphs the period and phase shift of Trigonometric Graphs The following diagrams show how to determine the transformation of a Trigonometric Graph from its equation. Scroll down the page for more examples and solutions. Amplitude Of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[388],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7747"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=7747"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/7747\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=7747"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=7747"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=7747"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"Transformation](\"https:\/\/www.onlinemathlearning.com\/image-files\/transformation-trig-graphs.png\" "\\"Transformation")
<\/figure>\n\n\n\nAmplitude Of Trigonometric Functions<\/h3>\n\n\n\n
Period of Trigonometric Function<\/h3>\n\n\n\n
![\"\"\/](\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-graphs_clip_image008.gif\")
<\/figure>\n\n\n\n
Find the period of the graph y = sin 2x and sketch the graph of y = sin 2x for 0 \u2264 2x \u2264 \u03c0.<\/p>\n\n\n\n
Since B = 2, the period is P = 2\u03c0\/B = 2\u03c0\/2 = \u03c0<\/p>\n\n\n\n![\"\"\/](\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-graphs_clip_image015.gif\")
<\/figure>\n\n\n\nPhase Shift of Trigonometric Functions<\/h3>\n\n\n\n
y = A sin B(x + C)
where A is the amplitude, the period is calculated by the constant B, and C is the phase shift.<\/p>\n\n\n\n
Find the amplitude, period and phase shift of<\/p>\n\n\n\n![\"\"\/](\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-graphs_clip_image017.gif\")
<\/figure>\n\n\n\n
Rewrite<\/p>\n\n\n\n![\"\"\/](\"https:\/\/www.onlinemathlearning.com\/image-files\/trigonometric-graphs_clip_image019.gif\")
<\/figure>\n\n\n\n
Periodic Functions Definition, Period, Phase Shift, Amplitude, Vertical Shift.
A periodic function is a function whose graph repeats itself identically from left to right.
The period of a function is the horizontal distance required for a complete cycle.
The period of a basic sine and cosine function is 2\u03c0.
The frequency of a function is the reciprocal of the period.
The phase shift of a function is the horizontal shift of a periodic function.
The amplitude of a function is half the distance between the maximum and minimum values of a periodic function. The amplitude is always positive.
The vertical shift of a function is the vertical shift of a periodic function along the y-axis.<\/p>\n","protected":false},"excerpt":{"rendered":"