Question

If $\cos \theta =\frac{9}{15}$ then find $\sin \theta$

Answer 1

$\cos \theta =\frac{9}{15}$ is positive.

$\therefore \theta$ lies in the first or fourth quadrant.

$\Rightarrow {\cos }^2\theta =\frac{81}{225}$

$\Rightarrow 1-{\cos }^2\theta =1-\frac{81}{225}$

$\Rightarrow {\sin }^2\theta =\frac{225-81}{225}$

$\Rightarrow {\sin }^2\theta =\frac{144}{225}$

$\therefore \sin \theta =\frac{12}{15}$ since $\sin \theta$ is negative in fourth quadrant and positive in first quadrant.