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Pre Calc Chapter 7

Pre Calc Chapter 7. Analytic Trig. Trigonometric Identities—7.1. Analytic Trigonometry. Reciprocal Identities Pythagorean Identities. Analytic Trigonometry. Even-Odd Identities Co-function Identities. Even-Odd Identities. Why does sin(-x) = -sin(x)??. Co-Function Identities.

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Pre Calc Chapter 7

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  1. Pre Calc Chapter 7 Analytic Trig

  2. Trigonometric Identities—7.1

  3. Analytic Trigonometry • ReciprocalIdentities • PythagoreanIdentities

  4. Analytic Trigonometry • Even-Odd Identities • Co-function Identities

  5. Even-Odd Identities Why does sin(-x) = -sin(x)??

  6. Co-Function Identities

  7. Co-Function Identities

  8. Co-Function Identities

  9. Co-Function Identities

  10. Co-Function Identities

  11. Simplifying With Identities

  12. Simplifying With Identities

  13. Proving Identities • Prove one side equals the other • Usually* try to modify the more difficult side • If stumped try working other side • Generally don’t want to “meet in the middle”

  14. Proving Identities

  15. Proving Identities

  16. p.540 # 9-33 Odd

  17. Addition and Subtraction—7.2

  18. Addition and Subtraction Identities

  19. Addition and Subtraction Identities • Proving Co-Function Identities

  20. Addition and Subtraction Identities

  21. Addition and Subtraction Identities

  22. p.548#1-4, 11-14, 17-19, 21-23

  23. Sums of Sines and Cosines • If A and B are real numbers, then: where and

  24. Sums of Sines and Cosines • Express the function in terms of sine only

  25. Sums of Sines and Cosines • Express the function in terms of sine only

  26. p.548# 29-31, 36, 39-42

  27. Double-Angle Formulas

  28. Double-Angle Formulas

  29. Double-Angle Formulas

  30. Double-Angle Formulas

  31. Power Reducing Formulas

  32. Power Reducing Formulas

  33. p.557#1-4, 9-11

  34. Half-Angle Formulas The choice of + or – depends on the quadrant of x/2

  35. Half-Angle Formulas

  36. Half-Angle Formulas

  37. p.557 # 15-20, 23-34

  38. Product to Sum Formulas

  39. Product to Sum Formulas • Re-write the following product as a sum

  40. Product to Sum Formulas • Find the value of the following

  41. Sum to Product Formulas

  42. Sum to Product Formulas • Re-write the following sum as a product

  43. Sum to Product Formulas • Find the value of the following

  44. p.558 # 35-60

  45. Inverse Trig Functions • What is an inverse function? • If f is one-to-one function with domain A and range B, then its inverse is a function with domain B and range A

  46. Inverse Trig Functions • Inverse sine function (arcsine)

  47. Inverse Trig Functions • Examples:

  48. Inverse Trig Functions • Inverse Cosine

  49. Inverse Trig Functions • Examples

  50. Inverse Trig Functions • Inverse Tangent

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