1. Trigonometry Chapters 8.2 - 8.3

2. 45-45-90 Theorem

3. The opposite sides of a 45-45-90 triangle are the same length Using the Pythagorean theorem we find the hypotenuse is always n times the square root of 2

4. 45-45-90 Theorem What is the length of the hypotenuse

5. 45-45-90 Theorem What is the length of the hypotenuse

6. 45-45-90 Theorem What is the length of the sides?

7. 45-45-90 Theorem What is the length of the sides? Remember, the hypotenuse is  2 times a side

8. Divide by  2 Rationalize the Denominator

10. 30-60-90 Theorem

11. The opposite of the 30 0 angle is n

12. 30-60-90 Theorem The opposite of the 60 0 angle is n  3

13. 30-60-90 Theorem The opposite of the right angle is 2n

14. 30-60-90 Theorem Find the lengths of the other two sides

15. 30-60-90 Theorem Find the lengths of the other two sides

16. 30-60-90 Theorem Find the lengths of the other two sides

17. 30-60-90 Theorem Find the lengths of the other two sides

18. 30-60-90 Theorem Find the lengths of the other two sides First find the length of side opposite the 30

19. 30-60-90 Theorem Call the side x x times  3 = 8

21. 30-60-90 Theorem Hypotenuse is 2 times the side opposite the 30 0 angle

22. Trigonometry Trigonometric Ratios- – Similar right triangles have equivalent ratios for its corresponding sides

23. Sine Sine of óB =

24. Sine Sine of óB =

25. Sine Sin B =

26. Cosine Cosine of óB =

27. Cosine Cosine of óB =

28. Cosine Cos B =

29. Tangent Tangent of óB =

30. Tangent Tangent of óB =

31. Tangent Tan B =

32. Trigonometry How to remember the order: Sin x = Cos x = Tan x =

33. Trigonometry Find the sine, cosine, and tangent ratios of ó B

34. Sin B = Cos B = Tan B =

35. Trigonometry What is the sin of ó B? Type it into a calculator: sin (40) Sin (40) =.64

36. How can we use this? Find the length of the hypotenuse. We’re given angle B and the opposite side

37. We know: We can plug in what we know: Find the length of the hypotenuse. Sin B = Sin 40 =

38. Solve: Sin 40 = Sin 40 =

39. Plug it into your calculator to find x Sin 40 = =

40. Find the length of the adjacent side. Cos B = Cos 40 =

41. Solve for x Cos 40 = Type into calculator 9.19 =

42. Find the length of the adjacent side. 9.19 =

43. Inverse Trig Functions Each trig function has an inverse that works like dividing. The inverse of sin is sin -1

44. Inverse Trig Functions

45. Find angle x Label the triangle

46. We have the opposite and hypotenuse Which one uses those two sides? Sin x = Cos x = Tan B =

47. Plug in the opposite and hypotenuse Sin x = Notice the x is in front of the sine, so we can’t just divide! Multiply by the inverse of sine

48. This cancels out the sine on the left Sin -1 (Sin x) = Sin -1