91Ó°ÊÓ

Prove that \(\arcsin x+\arccos x=\pi / 2\) if \(-1 \leq x \leq 1\).

Find a formula for \(\sin 3 a\) in terms of \(\sin a\) and \(\cos a\). Use it to calculate \(\sin \pi / 3\) and \(\cos \pi / 3 .\) Also calculate \(\sin \pi / 6\) and \(\cos \pi / 4\)

Suppose that \(f: \mathbb{R} \rightarrow \mathbb{R}\) and \(g: \mathbb{R} \rightarrow \mathbb{R}\) are periodic functions of period \(T .\) Under what conditions is the sum \(f+g: \mathbb{R} \rightarrow \mathbb{R}\) also periodic? Under what conditions is the composition \(f \circ g: \mathbb{R} \rightarrow \mathbb{R}\) periodic?