# Chapter 4 - Section 4.3 - Right Triangle Trigonometry - Exercise Set - Page 563: 86

a) The value of $\theta '$ is $15{}^\circ$. b) The value of $\theta '$ is $\frac{\pi }{6}$.

#### Work Step by Step

(a) The angle formed by a full rotation of the terminal side in degrees is $360{}^\circ$. The angle $\theta '$ is the difference between $360{}^\circ$ and $\theta$. $\theta '=360{}^\circ -\theta$ Put $345{}^\circ$ for $\theta$. \begin{align} & \theta '=360{}^\circ -345{}^\circ \\ & =15{}^\circ \end{align} (b) And the angle formed by a half rotation of the terminal side in radians is $\pi$. The angle $\theta '$ is the difference between $\pi$ and $\theta$. $\theta '=\pi -\theta$ Put $\frac{5\pi }{6}$ for $\theta$. \begin{align} & \theta '=\pi -\frac{5\pi }{6} \\ & =\frac{6\pi -5\pi }{6} \\ & =\frac{\pi }{6} \end{align}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.