select all functions that have a period $pi$.\n$square y = cos(\frac{x}{2})$\n$square y = sin(\frac{x}{2})$\n…

Explanation:

Step1: Recall period formula

The period of $y = A\sin(Bx)$ and $y=A\cos(Bx)$ is $T=\frac{2\pi}{|B|}$.

Step2: Analyze $y = \cos(\frac{x}{2})$

For $y = \cos(\frac{x}{2})$, $B=\frac{1}{2}$, so $T=\frac{2\pi}{\left|\frac{1}{2}\right|}=4\pi$.

Step3: Analyze $y = \sin(\frac{x}{2})$

For $y = \sin(\frac{x}{2})$, $B = \frac{1}{2}$, so $T=\frac{2\pi}{\left|\frac{1}{2}\right|}=4\pi$.

Step4: Analyze $y=\cos(x)$

For $y=\cos(x)$, $B = 1$, so $T=\frac{2\pi}{|1|}=2\pi$.

Step5: Analyze $y=\cos(2x)$

For $y=\cos(2x)$, $B = 2$, so $T=\frac{2\pi}{|2|}=\pi$.

Step6: Analyze $y=\sin(2x)$

For $y=\sin(2x)$, $B = 2$, so $T=\frac{2\pi}{|2|}=\pi$.

Answer:

$y = \cos(2x)$, $y=\sin(2x)$