Evaluating Trigonometric Functions Honors Algebra II Trigonometry

Essential Question: How do you evaluate trigonometric functions using reference angles? Essential Vocabulary: Reference Angle

Reference Angle A Reference Angle is the acute angle formed by the terminal side of 𝜃 and the x-axis. Reference angles are denoted by 𝜃 ′

Reference Angles Cont…. If 𝜃 is an angle in Quadrants II or III: Ask yourself: How far is it from 𝟏𝟖𝟎 ° 𝒐𝒓 𝝅? If 𝜃 is an angle in Quadrant IV: Ask yourself: How far is it from 𝟑𝟔𝟎 ° 𝒐𝒓 𝟐𝝅 ? Can we find a pattern with the angles on the Unit Circle?

D E G R E E S 45° -- ends in a 5 Ex: 45°, 135°, 225°, 315° 30° -- divisible by 3, not divisible by 6 (ignoring the 0 at the end) Ex: 30°, 150°, 210°, 330° 60° -- divisible by 3 and divisible by 6 Ex: 60°, 120°, 240°, 300° D E G R E E S

R A D I A N S 𝜋 6 -- (30°) denominator of 6 Ex: 𝜋 6 , 5𝜋 6 , 7𝜋 6 , 11𝜋 6 𝜋 4 -- (45°) denominator of 4 Ex: 𝜋 4 , 3𝜋 4 , 5𝜋 4 , 7𝜋 4 𝜋 3 -- (60°) denominator of 3 Ex: 𝜋 3 , 2𝜋 3 , 4𝜋 3 , 5𝜋 3 R A D I A N S

Homework Homework 9.6 Quiz tomorrow