4 4 Trig Functions of Any Angle Objectives

4. 4 Trig Functions of Any Angle Objectives: Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions

Trig Functions of Any Angle Given an angle in standard position with (x, y) a point on the terminal side of y (x, y) r Precalculus 4. 4 Trigonometric Functions of Any Angle x 2

Example 1 · Let (-3, 4) be a point on the terminal side of . Find the sine, cosine and tangent of . Precalculus 4. 4 Trigonometric Functions of Any Angle 3

Example 2 · Given · Find sin and sec Precalculus 4. 4 Trigonometric Functions of Any Angle 4

Reference Angles · Let be an angle in standard position. Its reference angle is the acute angle ’ formed by the terminal side of and the x-axis. ’ ’ Precalculus 4. 4 Trigonometric Functions of Any Angle ’ 5

Calculating Reference Angles ’ ’ Precalculus 4. 4 Trigonometric Functions of Any Angle ’ 6

Example 3 · Find the reference angle ’ · = 300° · = 2. 3 · = -135° Precalculus 4. 4 Trigonometric Functions of Any Angle 7

Evaluating Trig Functions of Any Angle To find the value of a trig function of any angle : 1. Evaluate the function for the associated reference angle ’. 2. Determine the sign of the trig function based on the quadrant in which lies. Precalculus 4. 4 Trigonometric Functions of Any Angle 8

Example 4 · Use reference angles to evaluate the trig function · · · Precalculus 4. 4 Trigonometric Functions of Any Angle 9

Example 5 · Let be an angle in Quadrant II such that sin =1/3. Find cos and tan by using trig identities. Precalculus 4. 4 Trigonometric Functions of Any Angle 10

Closure · Explain how to use reference angles to determine trig functions of any angle Precalculus 4. 4 Trigonometric Functions of Any Angle 11

Assignment · 4. 4 page 320: 3 -102 every 3 rd, 111, 112 Precalculus 4. 4 Trigonometric Functions of Any Angle 12

Bellwork 1. Find sin 4 7 2. Determine the sign (positive or negative) of the six trig functions for angles in Quadrant I, Quadrant III, and Quadrant IV Precalculus 4. 4 Trigonometric Functions of Any Angle 13