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.