Problem

(a) Sketch the graph of $y=3\sin x+2$ for $0\leq x\leq 2\pi$.

(b) Determine the number of solutions in the interval $0\leq x\leq 2\pi$ of each of the following equations.

(i) $3\sin x+2=x$

(ii) $3\sin x+2=5-x$

(c) Solve the equation $3\sin x+2=5\cos^2 x-1$ for $0\leq x\leq 2\pi$.