Name the quadrant in which the angle θ lies.
- $\tan \theta > 0 , \quad \sin \theta < 0$

Question

Name the quadrant in which the angle θ lies.
-$\tan \theta > 0 , \quad \sin \theta < 0$
A) I
B) II
C) III
D) IV

Quizplus · Accepted Answer

In the third quadrant, both sine and tangent are negative, but since the question specifies $\tan \theta > 0$ and $\sin \theta < 0$, it contradicts the usual signs. However, the correct interpretation based on the given conditions ($\tan \theta > 0$ and $\sin \theta < 0$) actually indicates the third quadrant, where tangent is positive due to both sine and cosine being negative (since $\tan \theta = \frac{\sin \theta}{\cos \theta}$), and sine is negative as specified.

Name the Quadrant in Which the Angle θ Lies tan⁡θ>0,sin⁡θ<0\tan \theta > 0 , \quad \sin \theta < 0tanθ>0,sinθ<0

Name the Quadrant in Which the Angle θ Lies $\tan \theta > 0 , \quad \sin \theta < 0$