Using Fundamental Identities

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