Question

(b) find an angle between 0 and 2\pi that is coterminal with \theta. write your answer in radians in terms of \pi. radians
(c) find an angle between - 2\pi and 0 that is coterminal with \theta. write your answer in radians in terms of \pi. radians

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles are given by $\theta + 2k\pi$, where $k$ is an integer.

Step2: For part (b)

Let $\theta$ be the given angle. We want to find an angle $\alpha$ such that $0\leq\alpha<2\pi$ and $\alpha=\theta + 2k\pi$. We choose $k$ such that $\alpha$ is in the desired range. For example, if $\theta = \frac{7\pi}{2}$, then $\frac{7\pi}{2}-2\pi=\frac{7\pi - 4\pi}{2}=\frac{3\pi}{2}$, and $0<\frac{3\pi}{2}<2\pi$.

Step3: For part (c)

We want to find an angle $\beta$ such that $- 2\pi<\beta<0$ and $\beta=\theta + 2k\pi$. If $\theta=\frac{7\pi}{2}$, then $\frac{7\pi}{2}-4\pi=\frac{7\pi - 8\pi}{2}=-\frac{\pi}{2}$, and $-2\pi<-\frac{\pi}{2}<0$.

Answer:

(b) Please provide the value of $\theta$ to get a specific answer.
(c) Please provide the value of $\theta$ to get a specific answer.