# How do you find the two quadrants that theta could terminate given costheta=1/2?

Apr 23, 2017

Quadrants $1$ and $4$.

#### Explanation:

Since $\cos \theta = \frac{1}{2}$, we know $\theta = \frac{1}{3} \pi$ or some complement of the angle. $\frac{1}{3} \pi$ is in the first quadrant and the equivalent angle which would give $\cos \theta = \frac{1}{2}$ is $2 \pi - \frac{1}{3} \pi = \frac{5}{3} \pi$ which is in the fourth quadrant.

As already stated, any complementary angles to these two would have to be in either quadrants $1$ or $4$.