The tutor offers a couple of illustrations of an important concept from trigonometry.

When an angle is drawn in standard position, it opens counterclockwise from the positive x axis.

Example 1: Show the angle 160° in standard position, along with its reference angle. Also label the quadrants.

The reference angle is always thought to be positive and is always measured from the x axis to where the angle finishes.

Example 2: Draw the angle in Quadrant III whose reference angle is 35°.

We see that the QIII angle with reference 35° has actual measure 215°.

The QIV angle with reference 35° is 325°.

HTH:)

Source:

Travers, Kenneth J et al. Using Advanced Algebra. Toronto: Doubleday Canada, 1977.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.