How would i Find cos(theta) if the terminal side goes through the point $(-1/3,1/2)$?

Question

How would i find cos theta $(-1/3 ,1/2)$ Find $\cos θ$? I tried making the triangle but nothing i do seems to come up with the correct answer.

Answer 1

Any time the point isn’t in the first quadrant, you have to use the extended definition of the trigonometric functions. Remember that $\cos\theta=x/r$, $\sin\theta=y/r$, and $\tan\theta=y/x$. In these formulas, $r$ is the distance of the point from the origin, always taken to be positive. For your angle, the distance is $\sqrt{1/9 + 1/4}=\sqrt{13/36}=\sqrt{13}/6$. Therefore your cosine is $$ \frac{-1/3}{\sqrt{13}/6}=-\frac2{\sqrt{13}}=-\frac{2\sqrt{13}}{13}\,. $$