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Section 13.3

Section 13.3. Evaluate Trigonometric Functions of Any Angle. 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.

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Section 13.3

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  1. Section 13.3 Evaluate Trigonometric Functions of Any Angle

  2. 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.

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

  4. Recall: Soh-Cah-Toa

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

  6. 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 . y (x,y) r x

  7. 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

  8. Key Concept – The Unit Circle

  9. Unit Circle

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

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

  12. Key Concept – Reference Angle Relationships

  13. Note: A S T C

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

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

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

  17. EXAMPLE 5: 17

  18. EXAMPLE 6: 18

  19. Homework Sec 13.3 WS

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