A random variable \(\xi\) has \(F(x)\) as its distribution function \((p(x)\) is the density function). Find the distribution function (density function) of the random variable:

(a) \(\eta=a \xi+b, a\) and \(b\) are real numbers;

(b) \(\eta=\xi^{-1}(\mathbf{P}\{\xi=0\}=0)\);

(c) \(\eta=\tan \xi\)

(d) \(\eta=\cos \xi ;\)

(e) \(\eta=f(\xi)\), where \(f(x)\) is a continuous monotone function without intervals of constancy.