Question

Suppose the point with coordinates $(-12,5)$ is on the terminal side of angle $\theta$, the value of the sine trigonometric function of $\theta$. is $\frac{a}{13}$ Find $a$

Answer 1

Here, $r=\sqrt{x^2+y^2}$

$=\sqrt{{(-12)}^2+5^2}$

$=\sqrt{144+25}=13$

Since terminal ray lies inthe second quadrant, we have

$\sin \theta =\frac{5}{13}$
Ans: a=5