## Trigonometry 7th Edition

$300^{\circ}$
Given- $\sin\theta$ = - $\frac{\sqrt 3}{2}$ , $\theta$ belongs to Q IV We will find reference angle of $\theta$ first using positive value $\frac{\sqrt 3}{2}$ and reference angle theorem- $\sin\theta$ = - $\frac{\sqrt 3}{2}$ = -$\sin 60^{\circ}$ (As $\sin 60^{\circ}$ = $\frac{\sqrt 3}{2}$ ) Therefore by reference angle theorem, $60^{\circ}$ is the reference angle for desired angle $\theta$ The desired angle $\theta$ is in Q IV, Also $0^{\circ}\leq \theta\lt 360^{\circ}$ Therefore- $\theta$ = $360^{\circ} - 60^{\circ}$ = $300^{\circ}$