1. 2.3 Evaluating Trigonometric Functions for any Angle
JMerrill, 2009

2. 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.

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

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

7. 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