Finding Reference Angles

Pre-Calculus · Axiom Academy

EXAMPLE Finding Reference Angles Work the acute angle each terminal side makes with the x-axis — one angle in every quadrant. The reference angle is the acute angle between the terminal side and the x-axis. Find for , , , and — one angle in each quadrant. The rule depends only on which quadrant the angle lands in: Nice work — you found the reference angle in all four quadrants, in both degrees and radians. Reference angle: the acute angle ( ) between the terminal side and the x-axis. The rule is set by the quadrant: Q1 uses , Q2 uses , Q3 uses , Q4 uses . Radians work the same way: swap for and for , so in Q2 gives . For an angle outside , first add or subtract full turns to land a coterminal angle in range, then apply the same quadrant rule.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.