1. Super Trig PowerPoint

3. Warm up Solve the following equations: 8= 20= 7= 15= 16= 32 X X 2 21 X64 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 Hypotenuse
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. But if we are working with this angle, we label the sides like this...
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. X A) B) C) What is the side marked with an X? ϴ Adjacent Opposite
Hypotenuse C)

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

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

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

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

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

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

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

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

17. X A) B) C) What is the side marked with an X? ϴ Hypotenuse Opposite
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 Sine Cosine tangent Sin Cos Tan
Name
“say”
Sine
Cosine
tangent
Abbreviation
Abbrev.
Sin
Cos
Tan
Ratio of an angle measure
Sinθ = opposite side
hypotenuse
cosθ = adjacent side
tanθ =opposite side
adjacent side

23. Let’s practice… B c a C b A 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. Practice some more…
Find tan A: A 8 4 A
Find tan A: 8

25. Ex. 1: Finding Trig Ratios
Fractions
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.
Angle R
opposite
Sin R =
hypotenuse
adjacent
cosR =
hypotenuse
opposite
tanR =
adjacent

27. Practice

28. Trigonometry-Day 3

29. With your partner, identify each of the following:
BELL WORK
With your partner, identify each of the following:
hypotenuse: _______
side opposite angle A: _______
side adjacent to angle A: _______
side opposite angle B: _______
side adjacent to angle B: _______ c A B C b 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. This question will use Sine
SOH CAH TOA
This question will use Sine O H
Sinϴ=
7cm X
Sin35= X 7
Hypotenuse
opposite
35˚

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

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

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

36. 10 multiple choice questions
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 5cm Opposite Sinϴ= Hypotenuse 5 Sin30= 10 30˚
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 5 10
Sin30=

51. Sin Example 1 7cm F Opposite Sinϴ= Hypotenuse F Sin42= 7 7 (Sin42)= F
42˚
We can use Sin as the question involves the Opposite length and the Hypotenuse
7cm F
The rule we use is:
Opposite
Hypotenuse
Sinϴ= F 7
Sin42=
7 (Sin42)= F
4.68 cm (2dp)= F

52. Sin Example 2 H 10cm Opposite Sinϴ= 10 Hypotenuse Sin17= H
17˚
We can use Sin as the question involves the Opposite length and the Hypotenuse H
10cm
The rule we use is:
Opposite
Hypotenuse
Sinϴ= 10 H
Sin17=
H x Sin17= 10
H= 10
Sin17
H= cm (1dp)

53. Cosine (cos) Adjacent Cosϴ= Hypotenuse Adjacent Hypotenuse 50˚
We use cosine when we have the Adjacent length and the Hypotenuse
Hypotenuse
The rule we use is:
Adjacent
Hypotenuse
Cosϴ=
Adjacent

54. Cos Example 1 9cm Adjacent Cosϴ= Hypotenuse A A Cos53= 9 9 x Cos53= A
53˚
We can use Cos as the question involves the Adjacent length and the Hypotenuse
9cm
The rule we use is:
Adjacent
Hypotenuse
Cosϴ= A A 9
Cos53=
9 x Cos53= A
5.42 cm (2dp)= A

55. Cos Example 2 H 9cm Adjacent Cosϴ= 9 Hypotenuse Cos17= H H x Cos17= 10
17˚
We can use Cos as the question involves the Adjacent length and the Hypotenuse H
9cm
The rule we use is:
Adjacent
Hypotenuse
Cosϴ= 9 H
Cos17=
H x Cos17= 10
H= 9
Cos17
H= cm (2dp)

56. Tangent (tan) Opposite Tanϴ= Adjacent 10cm 6.4cm (1dp) 50˚
We use tangent when we have the Opposite and Adjacent lengths.
10cm
The rule we use is:
Opposite
Adjacent
Tanϴ=
6.4cm (1dp)

57. Tan Example 1 11cm Opposite Tanϴ= O Adjacent O Tan53= 11 11 x Tan53= O
53˚
We can use Tan as the question involves the Adjacent and Opposite lengths
11cm
The rule we use is:
Opposite
Adjacent
Tanϴ= O O 11
Tan53=
11 x Tan53= O
14.6 cm (1dp)= O

58. Tan Example 2 A 21cm Opposite Tanϴ= Adjacent 21 Tan35= A A x Tan35= 21
35˚
We can use Tan as the question involves the Adjacent and Opposite lengths A
The rule we use is:
21cm
Opposite
Adjacent
Tanϴ= 21 A
Tan35=
A x Tan35= 21
A= 21
Tan35
A= cm (2dp)

59. There are a few ways to remember this
The three rules
So we have:
Opposite
Hypotenuse
Adjacent
Hypotenuse
Opposite
Adjacent
Sinϴ=
Cosϴ=
Tanϴ= O H A H O A
Sinϴ=
Cosϴ=
Tanϴ=
SOHCAHTOA
There are a few ways to remember this

60. Practice Use Sine to find the missing lengths on these triangles:
2. Use Cosine to find the missing lengths on these triangles:
3. Use Tangent to find the missing lengths on these triangles: H
15cm
60˚
Sinϴ=
Opposite
Hypotenuse O
50˚
17cm H
22cm
60˚
Cosϴ=
Adjacent
Hypotenuse
25cm
38˚ A
Tanϴ=
Opposite
Adjacent
60˚ O A
42˚
15cm
11cm

61. End Bell Work You have 10 minutes to complete yesterday’s classwork.
The trig tables are located on your desks.
10 minutes
End

62. Finding missing angles
Trigonometry Day 5
Finding missing angles

63. Some Old Hairy Camels Are Hairier Than Other Animals
SOHCAHTOA
Opposite
Hypotenuse
Adjacent
Hypotenuse
Opposite
Adjacent
Sinϴ=
Cosϴ=
Tanϴ=

64. Find the missing angle SOH CAH TOA 7cm 3cm ϴ
This question will use Sin O H
7cm
Sinϴ=
3cm
Sinϴ= 3 7
Hypotenuse
opposite
Sinϴ= ϴ
What angle would give us this answer?
You could use the ANS button on your calculator
Sin-1ANS= ϴ
Sin = ϴ
25.4˚ (1dp)= ϴ

65. Find the missing angle SOH CAH TOA 6cm ϴ 8cm
This question will use Tan O A
Tanϴ=
6cm ϴ
Tanϴ= 8 6
Adjacent
Tanϴ=1.25
What angle would give us this answer?
8cm
Opposite
Tan-11.25= ϴ
51.3˚ (1dp)= ϴ

66. Find the missing angle SOH CAH TOA 12cm 9cm ϴ
This question will use Cos A H
12cm
Cosϴ=
9cm ϴ
Cosϴ= 9 12
Hypotenuse
Adjacent
Cosϴ=0.75
What angle would give us this answer?
You could use the ANS button on your calculator
Cos-1ANS= ϴ
Cos-10.75= ϴ
41.4˚ (1dp)= ϴ

67. Practice Questions Answers: ϴ 23cm 35cm 11cm ϴ 10cm 17cm ϴ ϴ 18cm 12cm
50.2˚
28.6˚
59.1˚
52.3˚
63.4˚
65.4˚
40.9˚
Practice Questions ϴ
23cm
35cm
11cm ϴ
10cm
17cm ϴ ϴ
18cm
12cm
22cm ϴ
12cm
20cm
11cm
13cm ϴ ϴ ϴ
10cm
5cm
6cm
15cm

68. Let’s Review-Day 6 Write out the rule for Sine, Cosine and Tangent.
Make up your own way of remembering SOHCAHTOA

69. Find the missing lengths and angles
Answers:
8cm
22.2cm
48.6 ˚
41.8 ˚
58.1 ˚
16cm
42.7 ˚
19.5cm
11cm
19.3˚
41 ˚
21.6cm
60 ˚
11.7cm
55.5 ˚
49.8 ˚
Find the missing lengths and angles 1 2 3 ϴ 4
16cm X
12cm X
15cm
8cm
30˚
51˚ ϴ
14cm
17cm 5 6 7 8 ϴ ϴ
36cm
18cm
19cm X X
9cm
11.2cm
63˚
35˚
8.3cm 9 10 11 12
15cm
50˚ ϴ
46cm
53cm X
40cm X
43˚
28˚ X
23cm 16 13 14 15 ϴ
32cm ϴ
106cm
16cm X
61cm
74cm
18˚
36cm
81cm ϴ

70. Use sin, cos and tan to find the missing lengths, round them to 1 d
Use sin, cos and tan to find the missing lengths, round them to 1 d.p, and use that answer to work out the next length.
Side
Length (rounded to 1 dp) a b c d e f g h i a b c d e f g h i
10cm
30˚
40˚
50˚
35˚
45˚
42˚
27˚
38˚
51˚

71. Use sin, cos and tan to find the missing lengths, round them to 1 d
Use sin, cos and tan to find the missing lengths, round them to 1 d.p, and use that answer to work out the next length.
Side
Length (rounded to 1 dp) a 5 b
4.2 c
3.2 d
2.2 e
3.1 f
3.4 g
1.7 h
2.8 i
9.5
Side
Length (rounded to 1 dp) a b c d e f g h i a b c d e f g h i
10cm
30˚
40˚
50˚
35˚
45˚
42˚
27˚
38˚
51˚

72. Extra-Practice Answers: 3.1cm 6.1cm 5.1cm 17.1cm 4.5cm 8.6cm 20.5cm