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 states $\tan \theta > 0$ and $\sin \theta < 0$, it seems there was a mistake in my explanation. Correctly, tangent is positive in the first and third quadrants, but sine is only negative in the third and fourth quadrants. Therefore, for both conditions to be satisfied ($\tan \theta > 0$ and $\sin \theta < 0$), the angle must lie in the fourth quadrant, not the third. This correction addresses the error in quadrant identification based on the signs of tangent and sine.

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 $\tan \theta > 0 , \quad \sin \theta < 0$