Question

find values of two different angles coterminal with the given angle. one of your answers must be positive and the other must be negative

1. 187°
2. $\frac{2pi}{7}$

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles of an angle $\theta$ are given by $\theta + 360^{\circ}n$ (in degrees) or $\theta+2\pi n$ (in radians), where $n$ is an integer.

Step2: Find coterminal angles for $187^{\circ}$

For the positive coterminal angle, let $n = 1$. Then $\theta_{1}=187^{\circ}+360^{\circ}=547^{\circ}$.
For the negative coterminal angle, let $n=- 1$. Then $\theta_{2}=187^{\circ}-360^{\circ}=-173^{\circ}$.

Step3: Find coterminal angles for $\frac{2\pi}{7}$

For the positive coterminal angle, let $n = 1$. Then $\theta_{3}=\frac{2\pi}{7}+2\pi=\frac{2\pi + 14\pi}{7}=\frac{16\pi}{7}$.
For the negative coterminal angle, let $n=-1$. Then $\theta_{4}=\frac{2\pi}{7}-2\pi=\frac{2\pi-14\pi}{7}=-\frac{12\pi}{7}$.

Answer:

For $187^{\circ}$: Positive - $547^{\circ}$, Negative - $-173^{\circ}$
For $\frac{2\pi}{7}$: Positive - $\frac{16\pi}{7}$, Negative - $-\frac{12\pi}{7}$