# How do you find the values of theta given costheta=1/2?

##### 1 Answer
Dec 19, 2016

pi/3; (5pi)/3

#### Explanation:

$\cos \theta = \frac{1}{2}$
Trigonometric table of special arcs gives -->
$\theta = \frac{\pi}{3} \left(\mathmr{and} {60}^{\circ}\right)$
Unit circle gives another arc $\theta$ that has the same cos value $\left(\frac{1}{2}\right)$:
$\theta = - \frac{\pi}{3}$ , or $\theta = \frac{5 \pi}{3}$ (co-terminal).
Answers for $\left(0 , 2 \pi\right)$
pi/3; (5pi)/3