The direction at which the wind strikes a tower is a random variable \(\theta\) with density function \(f(\theta)=\) \(c \cos \theta,-\pi / 4 \leq \theta \leq \pi / 4\). The angle \(\theta\) is measured from due east.

(a) Evaluate \(c\). (b) Sketch the density as a function of \(\theta\). (c) Calculate the probability that \(\theta>|\pi / 4|\). (d) Calculate the probability that \(-\pi / 10<\theta \leq \pi / 10\). (e) Sketch the cumulative distribution function.