Find the sign of the following.
-$\tan \frac { \theta } { 2 }$, given that $\theta$ is in the interval $\left( 90 ^ { \circ } , 180 ^ { \circ } \right)$.
A) positive
B) negative

Question

Quizplus · Accepted Answer

In the interval $ (90^\circ, 180^\circ) $, $\theta$ is in the second quadrant where sine is positive and cosine is negative. Since $\tan \frac{\theta}{2} = \frac{\sin \frac{\theta}{2}}{\cos \frac{\theta}{2}}$, and both sine and cosine of $\frac{\theta}{2}$ will be positive in this interval (as $\frac{\theta}{2}$ will be in the first quadrant), the tangent of $\frac{\theta}{2}$ will be positive.

Find the Sign of the Following tan⁡θ2\tan \frac { \theta } { 2 }tan2θ​

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