Question

Answer question number 20. The question is in the image.Reference angle is the angle form by the terminal side and the x-axis.

Answer 1

Answer: We have to sketch the angle and find the reference angle for the 20:

`(8\pi)/(3)`

The reference angle is an angle between the terminal side of the angle and the x-axis.

`\theta_R=180^(\circ)-\theta`

The provided angle is:

`\begin{gathered} \theta=(8\pi)/(3)=480^(\circ) \\ \\ 480^(\circ)=480^(\circ)-360^(\circ)=120^(\circ) \\ \\ \theta=120^(\circ) \end{gathered}`

Sketch of the angle:

Therefore the reference angle is:

`\begin{gathered} \theta_R=180^(\circ)-\theta \\ \\ \theta_R=180^(\circ)-120^(\circ) \\ \\ \theta_R=60^(\circ) \end{gathered}`