Question

Find the reference angle of
`( - 13\pi)/(6)`

Answer 1

Reference angle

The reference angle of a given angle A is the acute angle that A forms with the x-axis

We need to calculate the reference angle of

`( - 13\pi)/(6)`

This angle is greater than any angle of a single turn on the trigonometric circle.

Let's convert the improper fraction to a mixed fraction:

`-(13\pi)/(6)=-2\pi-(\pi)/(6)`

-2π corresponds to a complete turn around the circle, so we can discard that part and take only the -π/6

Since it's a negative angle, it runs clockwise and is located at the IV quadrant. The reference angle is π/6 because it's the angle it forms with the x-axis.

We'll include an image of the angle below