# How do you use transformation to graph the cosine function and determine the amplitude and period of y=3cos(-1/2x)?

Sep 21, 2017

Cosine is an even function, so $\cos \left(- x\right) = \cos x$

i.e. $\cos \left(- \frac{x}{2}\right) = \cos \left(\frac{x}{2}\right)$

Now, the period of cosx is $2 \pi$ radians

Hence, as x/2 is a horizontal stretch of factor 2 our period is $4 \pi$ radians

Also, $- 1 \le \cos \left(\frac{x}{2}\right) \le 1$....i.e. amplitude 1

Hence, $- 3 \le 3 \cos \left(\frac{x}{2}\right) \le 3$...i.e. amplitude 3

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