Question

determine two coterminal angles (one positive and one negative) for each angle. give your answers in radians. (enter your answers as a comma - separated list.) (a) $\frac{5pi}{6}$ (b) $-\frac{9pi}{4}$

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles of an angle $\theta$ are given by $\theta + 2k\pi$, where $k\in\mathbb{Z}$.

Step2: Find coterminal angles for $\frac{5\pi}{6}$

For the positive coterminal angle, let $k = 1$. Then $\theta_1=\frac{5\pi}{6}+2\pi=\frac{5\pi + 12\pi}{6}=\frac{17\pi}{6}$.
For the negative coterminal angle, let $k=-1$. Then $\theta_2=\frac{5\pi}{6}-2\pi=\frac{5\pi - 12\pi}{6}=-\frac{7\pi}{6}$.

Step3: Find coterminal angles for $-\frac{9\pi}{4}$

For the positive coterminal angle, let $k = 1$. Then $\theta_3=-\frac{9\pi}{4}+2\pi=-\frac{9\pi}{4}+\frac{8\pi}{4}=-\frac{\pi}{4}$. Let $k = 2$, then $\theta_4=-\frac{9\pi}{4}+4\pi=-\frac{9\pi}{4}+\frac{16\pi}{4}=\frac{7\pi}{4}$.
For the negative coterminal angle, let $k=-1$. Then $\theta_5=-\frac{9\pi}{4}-2\pi=-\frac{9\pi}{4}-\frac{8\pi}{4}=-\frac{17\pi}{4}$.

Answer:

(a) $\frac{17\pi}{6},-\frac{7\pi}{6}$; (b) $\frac{7\pi}{4},-\frac{17\pi}{4}$