Question

If $\tan \theta =\frac{-4}{3}$ then $\sin \theta$ is

• A. $\pm \frac{1}{5}$
• B. $\pm \frac{4}{5}$
• C. $\pm \frac{3}{5}$
• D. $\pm \frac{2}{5}$

Answer 1

The correct option is B $\pm \frac{4}{5}$

Solution: The negative value of $\tan \theta$ implies that $\theta$ belongs to either II or IV quadrant.

If $\theta$ lies in second quadrant, $\sin \theta$ must be positive.

$\sin \theta =\frac{4}{5}$

If $\theta$ lies in IV quadrant, $\sin \theta$ must be negative.

$\sin \theta =\frac{-4}{5}$

Hence, $\sin \theta =\pm \frac{4}{5}$