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
[tex]\frac{ - 13\pi}{6}[/tex]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:
[tex]-\frac{13\pi}{6}=-2\pi-\frac{\pi}{6}[/tex]-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
