Evaluate Trigonometric Functions of Any Angle Section 13.3 Evaluate Trigonometric Functions of Any Angle

California Standard: Mathematical Analysis 9 California Standard: Mathematical Analysis 9.0 Students compute by hand, the values of the trigonometric functions. 2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Evaluate trigonometric functions of any angle.

Recall: Soh-Cah-Toa

The Six Trigonometric Functions Let be an acute angle of a right triangle. Then the six trigonometric functions of the angle are defined as follows.

Definitions of Trigonometric Functions of Any Angle Let be an angle in standard position with (x,y) a point on the terminal side of and . (x,y) x y r

EXAMPLE 1: Let (-4,3) be a point on the terminal side of an angle θ in standard position. Evaluate the six trigonometric functions of θ. 7

Key Concept – The Unit Circle

Unit Circle

EXAMPLE 2: Use the unit circle to evaluate the six trigonometric functions of θ=270° 10

U-TRY #1: Evaluate the six trigonometric functions of θ. Use the unit circle to evaluate the six trigonometric functions of θ=180°.

Key Concept – Reference Angle Relationships

Note: A S T C

EXAMPLE 3: Find the reference angle θ’ for (a) and (b) . 14

EXAMPLE 4: Evaluate (a) and (b) . 15

U-TRY #2: Sketch the angle. Then find its reference angle. a) b) c) d) 2) Evaluate without using a calculator.

EXAMPLE 5: 17

EXAMPLE 6: 18

Homework Sec 13.3 WS