Question

\[ \text{If } \tan\theta=-\frac43, \]

\[ \text{then } \sin\theta \text{ is equal to} \]

(a) \(-\frac45\) but not \(\frac45\)
(b) \(-\frac45\) or \(\frac45\)
(c) \(\frac45\) but not \(-\frac45\)
(d) none of these

Solution

\[ \tan\theta=\frac{\text{Perpendicular}}{\text{Base}} =-\frac43 \]

Take

\[ \text{Perpendicular}=4, \quad \text{Base}=-3 \]

or

\[ \text{Perpendicular}=-4, \quad \text{Base}=3 \]

\[ \text{Hypotenuse} = \sqrt{4^2+3^2} =5 \]

Therefore,

\[ \sin\theta=\frac45 \]

or

\[ \sin\theta=-\frac45 \]

\[ \sin\theta=-\frac45 \text{ or } \frac45 \]

Answer

\[ \boxed{-\frac45 \text{ or } \frac45} \]

Correct Option: (b)