Question

I need the answer to this use fractions and pi

Answer 1

We are to find the positive and negative angles that are coterminal with

`(2\pi)/(3)`

By definition

Coterminal Angles are angles that share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians

Hence,

The positive coterminal angle is

`(2\pi)/(3)+2\pi`

Simplifying this we get

`\begin{gathered} (2\pi)/(3)+2\pi \\ =(2\pi+6\pi)/(3) \\ =(8\pi)/(3) \end{gathered}`

Therefore, the positive coterminal angle is

`(8\pi)/(3)`

The negative coterminal angle is

`\begin{gathered} (2\pi)/(3)-2\pi \\ =(2\pi-6\pi)/(3) \\ =-(4\pi)/(3) \end{gathered}`

Therefore, the negative coterminal angle is

`-(4\pi)/(3)`