Question

draw the terminal side of an angle in standard position that measures $-\frac{5\pi}{4}$ radians. hint: first plot a point at the origin, then plot a second point anywhere on the terminal side answer the following in radians. the $\pi$ is already given. find a nonnegative angle that is coterminal. $\square\pi$ find a negative angle that is coterminal. $\square\pi$ 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 \(-\frac{5\pi}{4}\), we add \(2\pi\).

$$-\frac{5\pi}{4}+2\pi=-\frac{5\pi}{4}+\frac{8\pi}{4}=\frac{3\pi}{4}$$

Step2: Find negative coterminal angle

For a negative coterminal angle of \(-\frac{5\pi}{4}\), we subtract \(2\pi\).

$$-\frac{5\pi}{4}-2\pi=-\frac{5\pi}{4}-\frac{8\pi}{4}=-\frac{13\pi}{4}$$

Answer:

Non - negative coterminal angle: \(\frac{3\pi}{4}\), Negative coterminal angle: \(-\frac{13\pi}{4}\)