Question

Find the reference angle given: t= -5π/3.

Answer 1

The reference angle is
`(\pi)/(3)`

Explanation:

The given angle is
`t=-(5\pi)/(3)`

The reference angle is the acute angle, that a given angle makes with the x-axis.

First let us make a sketch of the given angle. See diagram in attachment.

Let
`\theta` be the reference angle of
`t=-(5\pi)/(3)`

Then, from the diagram, we need to subtract
`\theta` from
`-(5\pi)/(3)` to get to
`-2\pi`.

We can therefore write the following equation and solve for
`\theta`.

`\Rightarrow -(5\pi)/(3)-\theta=-2\pi`

We group like terms to get,

`\Rightarrow -\theta=-2\pi +(5\pi)/(3)`

We collect LCM to get,

`\Rightarrow -\theta=(-6\pi+5\pi)/(3)`

We simplify to get,

`\Rightarrow -\theta=-(\pi)/(3)`

We divide through by
`-1`

`\theta=(\pi)/(3)` to get,

The correct answer is D.