Question
If $$\tan \theta = - \frac{4}{3},$$ then $$\sin \theta $$ is
A.
$$ - \frac{4}{5}{\text{ but not }}\frac{4}{5}$$
B.
$$ - \frac{4}{5}{\text{ or }}\frac{4}{5}$$
C.
$$ \frac{4}{5}{\text{ but not }} - \frac{4}{5}$$
D.
None of these
Answer :
$$ - \frac{4}{5}{\text{ or }}\frac{4}{5}$$
Solution :
$$\tan \theta = - \frac{4}{3}$$
$$ \Rightarrow \,\,\theta \in $$ II quad or IV quad.
$$\eqalign{
& \therefore \,\,\,0 < \sin \theta < 1\,\,{\text{or }} - 1 < \sin \theta < 0 \cr
& \therefore \,\,\sin \theta \,\,{\text{may be }}\frac{4}{5}\,{\text{or }} - \frac{4}{5} \cr} $$