Find the sign of the following.
-$\sin \frac { \theta } { 2 }$, given that $\theta$ is in the interval $\left( 180 ^ { \circ } , 270 ^ { \circ } \right)$.
A) positive
B) negative

Question

Quizplus · Accepted Answer

In the interval $(180^\circ, 270^\circ)$, $\theta$ is in the third quadrant where sine is negative. However, $\frac{\theta}{2}$ will be in the interval $(90^\circ, 135^\circ)$, which is in the second quadrant where sine is positive.

Find the Sign of the Following sin⁡θ2\sin \frac { \theta } { 2 }sin2θ​

Find the Sign of the Following $\sin \frac { \theta } { 2 }$