$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\sin \theta = - \frac { 1 } { 2 }$
A) $210 ^ { \circ }$ and $330 ^ { \circ }$
B) $150 ^ { \circ }$ and $210 ^ { \circ }$
C) $60 ^ { \circ }$ and $300 ^ { \circ }$
D) $60 ^ { \circ }$ and $120 ^ { \circ }$

Question

Quizplus · Accepted Answer

The sine function is negative in the third and fourth quadrants. The reference angle for $\sin \theta = -\frac{1}{2}$ is $30^\circ$. Therefore, the angles in the interval $[0, 360^\circ)$ where sine is $-\frac{1}{2}$ are $180^\circ + 30^\circ = 210^\circ$ and $360^\circ - 30^\circ = 330^\circ$.

- sin⁡θ=−12\sin \theta = - \frac { 1 } { 2 }sinθ=−21​

- $\sin \theta = - \frac { 1 } { 2 }$