## Trigonometry (10th Edition)

$\theta=3^{\circ}$
1. Cosecant and sine are reciprocals $\csc\theta=\frac{1}{\sin\theta}$ 2. Rewrite cosencant as a sine $\sin(4\theta +2^{\circ})=\sin(3\theta+5^{\circ})$ 3.Since the sine values are equal, the angles themselves must be equal. $4\theta -3\theta= 5-2$ $\theta=3^{\circ}$