Answer
$T=4$
Work Step by Step
When we are presented with a function such as $sin(bx)$ and are asked to find the period, it is useful to make use of the following formula:
$\frac{2\pi}{T}=b$
The $T$ in the equation represents the period of the function, as in the amount of $x$ units before the function repeats itself.
In this question, we have $cos(\frac{\pi x}{2})$. Thus, $\frac{2\pi}{\frac{\pi}{2}}=T=4$ . Keep in mind that the formula above allows us to easily swap the $T$ and the $b$ in the formula, thus, the period of this function is $4$.
