Question

Determine the quadrant for an angle with the following characteristics: $\sin \theta <0\mathrm{and}\tan \theta <0$

• A. Quadrant I
• B. Quadrant II
• C. Quadrant III
• D. Quadrant IV

Answer 1

The correct option is D

Quadrant IV

Explanation for the correct option:

Finding the quadrant for $\mathbf{sin\theta }\mathbf{<}\mathbf{0}\mathbf{}\mathbf{}\mathbf{and}\mathbf{}\mathbf{tan\theta }\mathbf{<}\mathbf{0}$ :

$\sin \theta$ is positive in I and II quadrant and negative in III and IV quadrant.

$\tan \theta$ is positive in I and III quadrant and negative in II and IV quadrant

So both $\sin \theta$ and $\tan \theta$ is negative in the IV quadrant.

Hence, option (D) is the correct option.