If $\tan \theta=-\frac{4}{3}$, then the value of $\sin \theta$ is

• A

  $-\frac{4}{5}$ but $\neq \frac{4}{5}$
• Correct answer
  B

  $-\frac{4}{5}$ or $\frac{4}{5}$
• C

  $\frac{4}{5}$ but $\neq-\frac{4}{5}$
• D

  $\frac{1}{5}$

Solution

We have, $\tan \theta=-\frac{4}{3}$
$\because \tan \theta$ is less than 0 and $0 \lt \theta \lt \frac{\pi}{2}$ or $\quad \frac{3 \pi}{2} \lt \theta \lt 2 \pi$. $\therefore \sin \theta=\frac{\text { perpendicular }}{\text { hypotenuse }}=-\frac{4}{5}$ (i.e. - ve $)$ But, $\theta$ lies also between $\frac{3 \pi}{2}$ and $2 \pi$ $\therefore \quad \sin \theta=\frac{4}{5}$ also.

Hence, the correct answer is option: 'B'.