Super Trig PowerPoint

1. Super Trig PowerPoint

3. Warm up Solve the following equations: • 20= • 15= • 8= • 7= • 16= 32 X X 2 21 X X 3 64 X

4. Trigonometry • We can use trigonometry to find missing angles and lengths of triangles. • Trigonometry uses three functions, these are called: • Sine (shortened to Sin and pronounced “sign”) • Cosine (shortened to Cos) • Tangent (shortened to Tan) • We will start working with right angled triangles

5. Labelling the sides Before we can use Sin, Cos and Tan we need to be able to label the sides of a right angled triangle The longest side, the one opposite the right angle is called the hypotenuse Hypotenuse

6. Labelling the sides What we call the other two sides will change depending on which angle we are working with, for example.. If we are given (or need to work out) this angle, we label the other sides like this.. Adjacent Opposite But if we are working with this angle, we label the sides like this... ϴ Opposite Adjacent

7. Labelling Right Angle Triangle 10 multiple choice questions

8. What is the side marked with an X? X ϴ Adjacent Opposite A) B) Hypotenuse C)

9. What is the side marked with an X? ϴ X Hypotenuse Opposite A) B) Adjacent C)

10. What is the side marked with an X? X ϴ Hypotenuse Opposite A) B) Adjacent C)

11. What is the side marked with an X? ϴ X Opposite Adjacent A) B) Hypotenuse C)

12. What is the side marked with an X? X ϴ Adjacent Opposite A) B) Hypotenuse C)

13. What is the side marked with an X? X ϴ Opposite Adjacent A) B) Hypotenuse C)

14. What is the side marked with an X? ϴ X Opposite Adjacent A) B) Hypotenuse C)

15. What is the side marked with an X? ϴ X Opposite Hypotenuse A) B) Adjacent C)

16. What is the side marked with an X? ϴ X Hypotenuse Adjacent A) B) Opposite C)

17. What is the side marked with an X? X ϴ Hypotenuse Opposite A) B) Adjacent C)

18. Practice

19. Trigonometry-Day 2 • Bell work: Copy and Complete: Identify the opposite side and adjacent side from: • (a) Angle P (b) Angle R

20. Trigonometry-Rev. • We can use trigonometry to find missing angles and lengths of triangles. • Trigonometry uses three functions, these are called: • Sine (shortened to Sin and pronounced “sign”) • Cosine (shortened to Cos) • Tangent (shortened to Tan) • We will start by practicing writing the ratios for Sine, Cosine and Tangent

21. SOHCAHTOA

22. Trigonometric Ratios

23. Let’s practice… Write the ratio for sin A Write the ratio for cos A Write the ratio for tan A B c a C b A Let’s switch angles: Find the sin, cos and tan for Angle B:

24. 8 A 4 Practice some more… Find tan A: 24.19 12 A 21 Find tan A: 8

25. Ex. 1: Finding Trig Ratios opposite sin A = hypotenuse adjacent cosA = hypotenuse opposite tanA = adjacent

26. Ex. 2: Finding Trig Ratios—Find the sine, the cosine, and the tangent of the indicated angle. opposite Sin R = hypotenuse adjacent cosR= hypotenuse opposite tanR= adjacent

27. Practice

28. Trigonometry-Day 3

29. A b C B BELL WORK With your partner, identify each of the following: hypotenuse: _______ side opposite angle A: _______ side adjacentto angle A: _______ side opposite angle B: _______ side adjacentto angle B: _______ c a c b b a a

30. Skiers On Holiday Can Always Have The Occasional Accident SOHCAHTOA Opposite Hypotenuse Adjacent Hypotenuse Opposite Adjacent Sinϴ= Cosϴ= Tanϴ=

31. Our aim today • We have looked at the three rules and have practised labelling triangles. • Today we will have to decide whether we are using Sin, Cos or Tan when answering questions.

32. SOH CAH TOA This question will use Sine X 7 O H Sin35= Sinϴ= 7cm X Hypotenuse opposite 35˚

33. SOH CAH TOA This question will use Tan O A Tanϴ= Adjacent 17˚ 8 X Tan17= X 8cm opposite

34. SOH CAH TOA This question will use Sin O H Sinϴ= X 43˚ 8 X Sin43= Hypotenuse 8cm opposite

35. SOH CAH TOA This question will use Cosine A H cosϴ= Adjacent 26˚ X 8 Hypotenuse cos26= 8cm X

36. Sin, Cos or Tan? 10 multiple choice questions

37. Will you use Sin, Cos or Tan with this question? 11cm X 35˚ Cos Sin A) B) Tan C)

38. Will you use Sin, Cos or Tan with this question? 14˚ 15cm X Sin Tan A) B) Cos C)

39. Will you use Sin, Cos or Tan with this question? X 40˚ 17cm Sin Cos A) B) Tan C)

40. Will you use Sin, Cos or Tan with this question? 50˚ 5cm X Tan Sin A) B) Cos C)

41. Will you use Sin, Cos or Tan with this question? X 51˚ 6cm Cos Tan A) B) Sin C)

42. Will you use Sin, Cos or Tan with this question? X 16˚ 8cm Sin Tan A) B) Cos C)

43. Will you use Sin, Cos or Tan with this question? X 42˚ 14cm Sin Cos A) B) Tan C)

44. Will you use Sin, Cos or Tan with this question? X 35˚ 4cm Tan Cos A) B) Sin C)

45. Will you use Sin, Cos or Tan with this question? 63˚ 3.4cm X Cos Tan A) B) Sin C)

46. Will you use Sin, Cos or Tan with this question? X 5mm 71˚ Sin Tan A) B) Cos C)

47. Practice

48. Bell Work: Copy and complete • Late work is to be turned into the __________________located____________. • Class work that is due at the end of the period is turned into the ________________. • I need to bring to class a ___________, ____________ and a good ______________ 3 minutes

49. Trigonometry-Day 4 • We can use trigonometry to find missing angles and lengths of triangles. • Trigonometry uses three functions, these are called: • Sine (shortened to Sin and pronounced “sign”) • Cosine (shortened to Cos) • Tangent (shortened to Tan) • We will start by practicing writing the ratios for Sine, Cosine and Tangent

50. Sine (sin) 10cm We use Sine when we have the Opposite length and the Hypotenuse 5cm The rule we use is: Opposite Hypotenuse Sinϴ= Try entering sin30 in your calculator, it should give the same answer as 5 ÷ 10 30˚ 5 10 Sin30=