Express $3\sin x+4\cos x$ as $R\sin(x+\alpha)$. Hence solve \[ 3\sin x+4\cos x=2,\qquad 0^\circ\

Question

Express $3\sin x+4\cos x$ as $R\sin(x+\alpha)$. Hence solve $$ 3\sin x+4\cos x=2,\qquad 0^\circ\le x<360^\circ. $$

Accepted Answer

(a) $5\sin(x+53.1^\circ)$; (b) $x=103.3^\circ,330.4^\circ$.

Trigonometry