Question

draw the terminal side of an angle in standard position that measures $-\frac{7pi}{4}$ radians.
hint: first plot a point at the origin, then plot a second point anywhere on the terminal side.
answer the following using radians. the $pi$ is already given.
find a nonnegative angle that is coterminal. $squarepi$
find a negative angle that is coterminal. $squarepi$
question help: ebook message instructor

Explanation:

Step1: Find non - negative coterminal angle

Coterminal angles are found by adding or subtracting \(2\pi\).
For a non - negative coterminal angle of \(-\frac{7\pi}{4}\), we add \(2\pi\).

$$-\frac{7\pi}{4}+2\pi=-\frac{7\pi}{4}+\frac{8\pi}{4}=\frac{\pi}{4}$$

Step2: Find negative coterminal angle

For a negative coterminal angle of \(-\frac{7\pi}{4}\), we subtract \(2\pi\).

$$-\frac{7\pi}{4}-2\pi=-\frac{7\pi}{4}-\frac{8\pi}{4}=-\frac{15\pi}{4}$$

Answer:

Non - negative coterminal angle: \(\frac{\pi}{4}\)
Negative coterminal angle: \(-\frac{15\pi}{4}\)