Question

If $\tan \theta =-\frac{4}{3}$ and $\theta$ does not lie in the second quadrant, so the value of $\sin \theta$ is

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

Answer 1

The correct option is A $-\frac{4}{5}$

Given: $\tan \theta =-\frac{4}{3}$
So, $\theta$ lies in second or fourth quadrant,
$\sin \theta =\pm \frac{4}{\sqrt{3^2+4^2}}=\pm \frac{4}{5}$
As given that $\theta$ does not lie in the second quadrant, so
$\theta$ lies in fourth quadrant
$\therefore \sin \theta =-\frac{4}{5}$