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Using Fundamental Identities

Using Fundamental Identities. Objective: To recognize and use fundamental Trig Identities. Reciprocal Identities. We need to use the following relationships. Quotient Identities. We need to use the following relationships. Pythagorean Identities. We need to use the following relationships.

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Using Fundamental Identities

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  1. Using Fundamental Identities Objective: To recognize and use fundamental Trig Identities.

  2. Reciprocal Identities • We need to use the following relationships.

  3. Quotient Identities • We need to use the following relationships.

  4. Pythagorean Identities • We need to use the following relationships.

  5. Pythagorean Identities • We need to use the following relationships.

  6. Pythagorean Identities • We need to use the following relationships.

  7. Pythagorean Identities • We need to use the following relationships.

  8. Pythagorean Identities • We need to use the following relationships.

  9. Example 1 • Use the values secx = -3/2 and tan x > 0 to find the values of all six trigonometric functions.

  10. Example 1 • Use the values secx = -3/2 and tan x > 0 to find the values of all six trigonometric functions. • We know that if the secx = -3/2, the cosx = -2/3. We also know that cos is negative and the tan is positive, putting us in quadrant 3.

  11. Example 1 • Use the values secx = -3/2 and tan x > 0 to find the values of all six trigonometric functions. • We know that if the secx = -3/2, the cosx = -2/3. We also know that cos is negative and the tan is positive, putting us in quadrant 3. • We will use a pythagorean identity to find the sinx.

  12. Example 1 • We will now find all six functions.

  13. Example 1 • Use the values secx = -3/2 and tan x > 0 to find the values of all six trigonometric functions. • We know that if the secx = -3/2, the cosx = -2/3. We also know that cos is negative and the tan is positive, putting us in quadrant 3. • This means that x = -2, r = 3, and y = , so:

  14. Example 1 • Find all 6 trig values.

  15. Example 1 • Find all 6 trig values. • We are in quadrant 3.

  16. Example 1 • Find all 6 trig values. • We are in quadrant 3.

  17. Example 1 • Find all 6 trig values. • We are in quadrant 3.

  18. Example 2 • Simplify the following:

  19. Example 2 • Simplify the following: • Factor out a common factor.

  20. Example 2 • Simplify the following: • Factor out a common factor. • Use the Pyth. Identity

  21. Example 2 • Simplify the following: • Factor out a common factor. • Use the Pyth. Identity

  22. Example 3 • Factor each expression:

  23. Example 3 • Factor each expression: • Look at this is terms of x.

  24. Example 3 • Factor each expression: • Look at this is terms of x.

  25. Example 3 • Factor each expression:

  26. Example 3 • Factor each expression: • Look at this is terms of x.

  27. Example 3 • Factor each expression: • Look at this is terms of x.

  28. You Try • Factor the expression.

  29. You Try • Factor the expression.

  30. You Try • Factor the expression.

  31. Example 6 • Perform the addition and simplify.

  32. Example 6 • Perform the addition and simplify. • Find a common denominator and add.

  33. Example 6 • Perform the addition and simplify. • Find a common denominator and add.

  34. Example 7 • Simplify each expression.

  35. Example 7 • Simplify each expression. • Try to put everything in terms of sin and cos and then simplify.

  36. Example 7 • Simplify each expression. • Try to put everything in terms of sin and cos and then simplify.

  37. Example 7 • Simplify each expression. • Try to put everything in terms of sin and cos and then simplify.

  38. Example 7 • Simplify each expression. • Try to put everything in terms of sin and cos and then simplify.

  39. You Try • Simplify each expression.

  40. You Try • Simplify each expression.

  41. You Try • Simplify each expression.

  42. Group Work • Work in groups/pairs to answer the following. • Page 541 • 2, 6 • 15-20 all • 28-34 even • 46, 50, 52

  43. Homework • Page 541 • 1, 3, 11, 13 • 21-26 all (answer to 26 is d) • 27-35 odd • 45, 47, 51, 53, 57, 59

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