Radio communications system - Uniform density question

Question

Full question: In a radio communications system, the phase difference $X $ between the transmitter and receiver is modeled as having a uniform density in $[—\pi, +\pi]$. Find $P(X \le 0)$ and $P(X \le \frac{\pi}{2})$.

Answer 1

Hint. The probability density function of $X$ is $$ f(x)=\begin{cases} \frac{1}{2\pi} & \mathrm{for}\ -\pi \le x \le \pi, \\[8pt] 0 & \mathrm{for}\ x<-\pi\ \mathrm{or}\ x>\pi \end{cases} $$ then you have $$ P(X\leq0)=\int_{-\infty}^0f(x)\:dx $$ $$ P\left(X\leq \frac{\pi}{2}\right)=\int_{-\infty}^{\pi/2}f(x)\:dx. $$ Can you take it from here?