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.