Question

draw the terminal side of an angle in standard position that measures $-2\pi$ 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. $\pi$
find a negative angle that is coterminal. $\pi$
question help: ebook message instructor

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles are given by \(\theta + 2k\pi\), where \(k\in\mathbb{Z}\) ( \(k\) is an integer).

Step2: Find a non - negative coterminal angle

Let \(k = 1\) for the angle \(\theta=-2\pi\).
Using the formula \(\theta + 2k\pi\), we substitute \(\theta=-2\pi\) and \(k = 1\):
\(-2\pi+2\times1\times\pi\)
\(=-2\pi + 2\pi=0\pi\)

Step3: Find a negative coterminal angle

Let \(k=-1\) for the angle \(\theta=-2\pi\).
Using the formula \(\theta + 2k\pi\), we substitute \(\theta=-2\pi\) and \(k=-1\):
\(-2\pi+2\times(-1)\times\pi\)
\(=-2\pi-2\pi=-4\pi\)

Answer:

Non - negative coterminal angle: \(0\pi\)
Negative coterminal angle: \(-4\pi\)