First slide

Trigonometric Identities

Question

If $\tan θ = - 4 / 3$ , then $\sin θ$ is

Moderate

A

- 4/5 but not 4/5
B

-4/5 or 4/5
C

4/5 but not - 4/5
D

none of these

Solution

We have,
$\tan θ < 0$
$\Rightarrow θ$ lies either in $II$ quadrant or $I V$ quadrant
$\begin{array}{l} \Rightarrow \sin θ > 0 or, \sin θ < 0 \\ ∴ \tan θ = - \frac{4}{3} \Rightarrow \sin θ = \pm \frac{4}{5} \Rightarrow \sin θ = \frac{4}{5} or, \sin θ = - \frac{4}{5} \end{array}$

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