Question

Find the measure of the reference angle for 0 theta = 290°

Answer 1

Definition of reference angle:

The smallest angle that the terminal side of a given angle makes with the x-axis.

Given that the angle theta is

`\theta=290^0`

Hence,

To figure out the reference angle, we will have

Assuming a base side for the angle along the X-axis, the reference angle is the smallest acute angle as measured from the X-axis

`\begin{gathered} reference\text{ angle =360}^0-290^0 \\ reference\text{ angle =70}^0 \end{gathered}`

(yes; I know this is not technically an acute angle, but it is the smallest positive angle).

Therefore,

The reference angle is = 70°