Given the random variables

\[ \begin{aligned} & U=\cos \Theta \\ & V=\sin \Theta \end{aligned} \]

with

\[ p_{\Theta}(\theta)= \begin{cases}1 / \pi & -\frac{\pi}{2}<\theta \leq \frac{\pi}{2} \\ 0 & \text { otherwise }\end{cases} \]

show that the correlation coefficient \(ho_{U V}=0\).