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 can be found by adding or subtracting \(2\pi n\) (where \(n\) is an integer) to the given angle \(\theta\). The formula is \(\theta + 2\pi n\).

Step2: Find a non - negative coterminal angle

Given \(\theta=- 2\pi\). Let \(n = 1\). Then \(\theta+2\pi n=-2\pi + 2\pi\times1\).

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Step3: Find a negative coterminal angle

Let \(n=-1\). Then \(\theta + 2\pi n=-2\pi+2\pi\times(-1)\).

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Answer:

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