Question

Determine two coterminal angles (one positive and one negative) for each angle. Give your answer in radians. (Enter you answer as a comma-separated list)

Answer 1

The answer is below

Explanation:

Coterminal angles are angles with the same terminal side at standard position (angles with the initial side on the positive x-axis). Coterminal angles may have different magnitude but they would have equal sides and vertices.

Coterminal angles can either be positive or negative. The positive coterminal is gotten by adding 2π rad or 360° while the negative coterminal is gotten by subtracting 2π rad or 360°.

a)

Positive coterminal angle =
`(5\pi)/(4)+2\pi=(13\pi)/(4) \ rad`

Negative coterminal angle =
`(5\pi)/(4)-2\pi=(-3\pi)/(4) \ rad`

b)

Positive coterminal angle =
`(-9\pi)/(4)+2\pi=(-\pi)/(4)+2\pi=(7\pi)/(4) \ rad`

Negative coterminal angle =
`(-9\pi)/(4)-2\pi=(-17 \pi)/(4) \ rad`