Question

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

• A. $\frac{-4}{5}$ but not $ \frac{4}{5}$
• B. $\frac{-4}{5}$ or $ \frac{4}{5}$
• C. $\frac{4}{5}$ but not $ - \frac{4}{5}$
• D. None of these

Answer 1

Answer: (B)

Since $\tan \, \theta = - \frac{4}{3}$ is negative, $\theta$ lies either in second quadrant or in fourth quadrant .
Thus $\sin \theta = \frac{4}{5}$ if $\theta$ lies in the second quadrant
or $\sin \theta = - \frac{4}{5}$ if $\theta$ lies in the fourth quadrant.