Question

draw the terminal side of an angle in standard position that measures 2π 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 π is already given.
find a nonnegative angle that is coterminal. π
find a negative angle that is coterminal. π
question help: ebook message instructor

Explanation:

Step1: Recall the formula for coterminal angles

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

Step2: Find a non - negative coterminal angle

Let \(k = 1\). Then \(\theta=2\pi\), and using the formula \(\theta + 2k\pi\), we have \(2\pi+2\times1\times\pi=4\pi\)

Step3: Find a negative coterminal angle

Let \(k=-1\). Then using the formula \(\theta + 2k\pi\) with \(\theta = 2\pi\), we get \(2\pi+2\times(- 1)\times\pi=0\) (not negative). Let \(k = - 2\), then \(2\pi+2\times(-2)\times\pi=2\pi - 4\pi=-2\pi\)

Answer:

Non - negative coterminal angle: \(4\pi\)
Negative coterminal angle: \(-2\pi\)