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

Precalculus 4.4 Trigonometric Functions of Any Angle 2 Trig Functions of Any Angle Given an angle  in standard position with (x,y) a point on the terminal side of  r (x,y)  y x

Precalculus 4.4 Trigonometric Functions of Any Angle 3 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 4 Example 2 ·Given ·Find sin  and sec 

Precalculus 4.4 Trigonometric Functions of Any Angle 5 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 6 Calculating Reference Angles  ’’  ’’  ’’

Precalculus 4.4 Trigonometric Functions of Any Angle 7 Example 3 ·Find the reference angle  ’ ·  = 300° ·  = 2.3 ·  = -135°

Precalculus 4.4 Trigonometric Functions of Any Angle 8 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 9 Example 4 ·Use reference angles to evaluate the trig function ·

Precalculus 4.4 Trigonometric Functions of Any Angle 10 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 11 Closure ·Explain how to use reference angles to determine trig functions of any angle

Precalculus 4.4 Trigonometric Functions of Any Angle 12 Assignment ·4.4 page 320: every 3rd, 111, 112

Precalculus 4.4 Trigonometric Functions of Any Angle 13 Bellwork 1.Find sin  2.Determine the sign (positive or negative) of the six trig functions for angles in Quadrant I, Quadrant II, Quadrant III, and Quadrant IV 4 7 