Question

Name a positive angle between 0 radians and 2π radians that is coterminal with an angle in standard position whose measure is −3π2 radians.

Answer 1

The positive angle between
`0` and
`2\pi` radians that is coterminal with
`\theta = -(3\pi)/(2)\,rad` is
`\theta = (\pi)/(2)\,rad`.

Explanation:

GIven that the measure of the known angle is
`-(3\pi)/(2)` radians and that such angle belongs to a set of angles in terms of revolutions (with a period of
`2\pi`) done either clockwise or counterclockwise, we can represent the family of coterminal angles with the following expression:

`\theta = -(3\pi)/(2)\pm (2\pi\cdot i)`, for
`i \in \mathbb{N}_(O)` (1)

Where
`i` is the index of the coterminal angle.

According to the statement, we must name a positive angle between
`0` and
`2\pi` radians, which can be found by the sign
`+` and
`i = 1`. Hence, we find the required angle:

`\theta = -(3\pi)/(2) + 2\pi`

`\theta = (\pi)/(2)\,rad`

The positive angle between
`0` and
`2\pi` radians that is coterminal with
`\theta = -(3\pi)/(2)\,rad` is
`\theta = (\pi)/(2)\,rad`.