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

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Answer 1 · 2017-09-21T08:11:53

Cosine is an even function, so $cos (- x) = cos x$ $cos(-x) = cosx$

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

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

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

Also, $- 1 \leq cos (\frac{x}{2}) \leq 1$ $-1 <= cos(x/2) <= 1$ ....i.e. amplitude 1

Hence, $- 3 \leq 3 cos (\frac{x}{2}) \leq 3$ $-3 <= 3cos(x/2) <= 3$ ...i.e. amplitude 3

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