$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\sin \theta = - \frac { \sqrt { 2 } } { 2 }$
A) $45 ^ { \circ }$ and $225 ^ { \circ }$
B) $225 ^ { \circ }$ and $315 ^ { \circ }$
C) $45 ^ { \circ }$ and $315 ^ { \circ }$
D) $135 ^ { \circ }$ and $225 ^ { \circ }$

Question

Quizplus · Accepted Answer

The sine function is negative in the third and fourth quadrants, corresponding to angles of $225 ^ { \circ }$ and $315 ^ { \circ }$, respectively.

- sin⁡θ=−22\sin \theta = - \frac { \sqrt { 2 } } { 2 }sinθ=−22​​

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