# Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set - Page 576: 100

The two values of $\theta$ are $\frac{\pi }{3}$ and $\frac{5\pi }{3}$.

#### Work Step by Step

We have the given expression: $\cos \theta =\frac{1}{2}$. Here, the reference angle is $\frac{\pi }{3}$ and $\theta$ lies in quadrants I or IV. Consider: the angle $\theta$ lies in quadrant I. $\theta =\frac{\pi }{3}$ Or the angle $\theta$ lies in quadrant IV. \begin{align} & \theta =2\pi -\frac{\pi }{3} \\ & =\frac{6\pi -\pi }{3} \\ & =\frac{5\pi }{3} \end{align}

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