# If tan

Question:

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

(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

Solution:

Given $\tan \theta=-\frac{4}{3}$

Since tan is negative in 2nd or 4th quadrant

⇒ θ lies in 2nd or 4th quadrant

Since AC2 = AB2 + BC2 = (–4)2 + (3)2

AC2 = 25

AC = ± 5

i.e. AC = 5

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

Hence, the correct answer is option B.