Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of $y=a \cdot \cos{[b(x-d)]}$ has:
amplitude = $|a|$
period = $\frac{2\pi}{b}$
phase shift = $|d|$, to the left when $d\lt0$, to the right when $d\gt0$
Write the given function in the form $y=a \cdot \cos{[b(x-d)]}$ by factoring out $\frac{1}{2}$ inside the cosine function to obtain:
$y=\frac{1}{2}\cos{[\frac{1}{2}(x-\frac{\pi}{2})]}$
The given function has:
$a=\frac{1}{2}$
$b=\frac{1}{2}$
$d=\frac{\pi}{2}$
Thus, the given function has:
amplitude = $|\frac{1}{2}|=\frac{1}{2}$
period = $\frac{2\pi}{\frac{1}{2}} = 4\pi$
phase shift = $|\frac{\pi}{2}|=\frac{\pi}{2}$ to the right
Therefore, the graph of the given function has the following properties/characteristics:
amplitude = $\frac{1}{2}$ so the y-values range from $-\frac{1}{2}$ to $\frac{1}{2}$
phase shift = $\frac{\pi}{2}$ units to the right
one period interval = $[\frac{\pi}{2}, \frac{9\pi}{2}]$
Refer to the graph in the answer part above.