2.3 Evaluating Trigonometric Functions for any Angle JMerrill, 2009

Reference Angles Reference Angle: the smallest positive acute angle determined by the x-axis and the terminal side of θ ref angle ref angle ref angle ref angle Think of the reference angle as a “distance”—how close you are to the closest x-axis.

Find Reference Angle 150° 30° 225° 45° 300° 60°

Using Reference Angles a) sin 330° = = - sin 30° = - 1/2 b) cos 120° = = - cos 60° = - ½

Using Reference Angles c) sin (-120°)= = - sin 60° Find the exact value of tan 495o To find the correct quadrant, find the smallest positive coterminal angle. 495o - 360o = 135o tan 495o = tan 135o. 135o is in Quad. II where tangent is negative. The reference angle = 45o tan 495o = - tan 45o = -1