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Trigonometric Functions of Any Angle (Section 4-4)

Learn to determine the exact values of trigonometric functions for any angle, identify quadrants, evaluate functions, find reference angles, and solve equations. Practice problems included.

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Trigonometric Functions of Any Angle (Section 4-4)

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  1. Trigonometric Functions of Any Angle (Section 4-4)

  2. Determine the exact value of the six trigonometric functions of the angle θ. Example 1

  3. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. Example 2 (2, -3)

  4. State the quadrant in which θ lies. Example 3 sin θ > 0 and cosθ < 0

  5. State the quadrant in which θ lies. Example 4 sec θ < 0 and tan θ > 0

  6. Find the values of the six trigonometric functions of θ. Example 5 θ lines in Quadrant III

  7. Find the values of the six trigonometric functions of θ. Example 6

  8. The terminal side of θ lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of θ by finding a point on the line. Example 7 Quadrant III

  9. Evaluate the trig function of the quadrant angle. Example 8 a) sin π b) c)

  10. Find the reference angle θ’ for the special angle θ. Then sketch θ and θ’ in standard position. Example 9 θ = 300°

  11. Find the reference angle θ’ for the special angle θ. Then sketch θ and θ’ in standard position. Example 10 θ = -135°

  12. Find the reference angle θ’. Then sketch θ and θ’ in standard position. Example 11 θ = 323°

  13. Find the reference angle θ’. Then sketch θ and θ’ in standard position. Example 12 θ =2.3

  14. HW #17 pg 294- 295 (1- 51 odd)

  15. Pg 291

  16. Evaluate the sine, cosine, and tangent of the angle without using a calculator. Example 13

  17. Evaluate the sine, cosine, and tangent of the angle without using a calculator. Example 14

  18. Evaluate the sine, cosine, and tangent of the angle without using a calculator. Example 15

  19. Find the indicated trigonometric value in the specified quadrant. Example 16 Function Quadrant Trigonometric Value II cosθ

  20. Find the indicated trigonometric value in the specified quadrant. Example 17 Function Quadrant Trigonometric Value III tan θ

  21. Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle. Example 18

  22. Use a calculator to evaluate the trigonometric function. (Be sure your calculator is set in the correct angle mode.) Example 19

  23. Use a calculator to evaluate the trigonometric function. (Be sure your calculator is set in the correct angle mode.) Example 20

  24. Use a calculator to evaluate the trigonometric function. (Be sure your calculator is set in the correct angle mode.) Example 21

  25. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 22

  26. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 23

  27. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 24

  28. Find two solutions to the equation. Give your answers in degrees (0< θ < 360) and radians (0< θ < 2). Do not use a calculator. Example 25

  29. Find the exact value of each function for the given angle for f(θ) = sin θ and g(θ) = cosθ. Do not use a calculator. Example 26 f(θ) + g(θ) e) 2f(θ) f(θ) – g(θ) f) g(-θ) [g(θ)]2 f(θ) g(θ)

  30. HW #18 pg 295 (53 – 107 odd)

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