Answer
$\theta=\cos^{-1}(\dfrac{10}{\sqrt{9 \pi^2+16 \pi}})$
Work Step by Step
Let us consider that $\theta$ be an angle between the vectors $f$ and $g$, which can be written as: $\cos \theta=\dfrac{\langle f,g\rangle}{\|g\|\|g\|}$
Since, we have
$\cos \theta=\dfrac{5}{(\dfrac{\sqrt \pi}{2})(\sqrt {9 \pi+16})}=\dfrac{10}{\sqrt{9 \pi^2+16 \pi}}$
So, the angle between $f$ and $g$ is equal to $\theta=\cos^{-1}(\dfrac{10}{\sqrt{9 \pi^2+16 \pi}})$
