# What is the period for y=-5cos(1/2)x?

The period of $\cos \left(\frac{x}{2}\right)$is 4pi because:
$\cos \left(x + 2 \pi\right) = \cos \left[\frac{1}{2} \left(x + 4 \pi\right)\right] = \cos \left(\frac{x}{2}\right)$