Answer
$\dfrac{\sqrt2}{4}$
Work Step by Step
RECALL:
$(f \circ h)(x)=f\left(h(x)\right)$
Use the rule above to obtain:
$(p\circ g)(315^\circ)=p\left(g(315^\circ)\right)=p(\cos{315^\circ})=p\left(\dfrac{\sqrt2}{2}\right)=\dfrac{\frac{\sqrt2}{2}}{2}=\dfrac{\sqrt2}{4}$
