Chapter 8, Problem 8.3P

Sketch an appropriate cross section of the radiation pattern and determine the beamwidth BW, pattern solid angle, and directivity for the following normalized radiation intensities:(a) $P_{\text{n}}\left(\theta ,\varphi \right)=\cos \theta$ for $0\le \theta \le \pi /2$, 0 otherwise;(b) $P_{\text{n}}\left(\theta ,\varphi \right)={\cos }^2\theta$ for $0\le \theta \le \pi /2$, 0 otherwise;(c) $P_{\text{n}}\left(\theta ,\varphi \right)={\cos }^3\theta$ for $0\le \theta \le \pi /2$, 0 otherwise.