Which transformations are needed to change the parent cosine function to y = 3cos (10 (x-pi)) ?

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Mathematics

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14 January, 08:41

Which transformations are needed to change the parent cosine function to y = 3cos (10 (x-pi)) ?

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Marie Patton · Answer 1

The parent cosine function can be transformed and translated. So, from the basic function cos (x) we can obtain function acos (bx+c). In our case, a=3 - amplitude, b=10 - the period change and c=-pi - the phase shift. So, the parent cosine function is mutiplied with 3 (which gives the amplitude of the function, 3*0.5=1.5). The period of the function is changed, and is 2pi/b=2pi/10=pi/5 and the cos (x) is phase shifted for c/b=-pi/10.