1. Use of Sine, Cosine and Tangent
TRIGONOMETRY
Use of Sine, Cosine and Tangent

2. SIMILAR TRIANGLE REVISION
Similar triangles have corresponding angles that are equal
The sides in one triangle are in a given ratio to the sides in the other triangle.
The larger triangles are scaled up versions of the small triangle.
RATIO = 2
1.5 cm
RATIO = 3
1cm Ө
3 cm
1.12 cm
2 cm
4.5 cm
3 cm Ө
2.24 cm Ө
3.36 cm

3. SIMILAR TRIANGLE REVISION
Similar triangles have corresponding angles equal
The sides in one triangle are in a given ratio to the sides in the other triangle.
The larger triangles are scaled up versions of the small triangle.

4. SIMILAR TRIANGLE REVISION
The larger triangles are scaled up versions of the small triangle.

5. TRIGONOMETRY some definitions
The side opposite the angle Ө is the Opposite side (Opp)
The side opposite the Right angle is the Hypotenuse (Hyp)
The side next to the angle is the Adjacent (Adj)
Hypotenuse
Opposite Ө
Adjacent

6. TRIGONOMETRY
Hypotenuse
Opposite Ө
Adjacent

7. TRIGONOMETRY
Hypotenuse
Opposite Ө
Adjacent

8. TRIGONOMETRY
Remember: The sides in one triangle are in a given ratio to the sides in the other triangle.
BUT: The sides within the one triangle are also related to each other in ratios which depend on the angle Ө.
RATIO = 2
1.5 cm
RATIO = 3
1cm Ө
3 cm
1.12 cm
2 cm
4.5 cm
3 cm Ө
2.24 cm Ө
3.36 cm

9. TRIGONOMETRY - Sine
The sides within the one (right angled) triangle are related to each other in ratios which depend on the angle Ө.
Opp = = = = Sine Ө =
Hyp
0.67
1.5 cm
1cm Ө
3 cm
1.12 cm
2 cm
4.5 cm
3 cm Ө
2.24 cm Ө
3.36 cm

10. TRIGONOMETRY - Cosine
The sides within the one (right angled) triangle are related to each other in fixed ratios which depend on the angle Ө.
Adj = = = = Cosine Ө =
Hyp
0.74
1.5 cm
1cm Ө
3 cm
1.12 cm
2 cm
4.5 cm
3 cm Ө
2.24 cm Ө
3.36 cm

11. TRIGONOMETRY - Sine
For right angled triangles, these ratios have been recorded
and are stored in your calculator
Opp = 2 = = Sine Ө = Sin Ө = Sin42˚
Hyp
Angle Ө = 42 degrees
3 cm
2 cm
2.24 cm

12. TRIGONOMETRY - Cosine Adj = 2.24 = 0.74 = Cosine Ө = Cos Ө = Cos42˚
Hyp
Angle Ө = 42 degrees
3 cm
2 cm
2.24 cm

13. TRIGONOMETRY - Tangent
Opp = 2 = = Tangent Ө = Tan Ө = Tan42˚
Adj
Angle Ө = 42 degrees
3 cm
2 cm
2.24 cm

14. Can you guess what X could be?
TRIGONOMETRY
Any right angled triangle with an angle of 42 ˚ will have sides in the same ratio as these triangles.
Can you guess what X could be?
Angle Ө = 42 degrees
X metres
(Opposite)
100 metres
(Adjacent)

15. TRIGONOMETRY Tan42˚ = Opp = X Adj 100 . . 0.89 = X 100
X = 89 metres
Angle Ө = 42 degrees
X metres
(Opposite)
100 metres
(Adjacent)

16. Can you guess what Y could be?
TRIGONOMETRY
Can you guess what Y could be?
89 m
Angle Ө = 42 degrees
Y metres

17. TRIGONOMETRY Can you guess what Y could be? Tan42˚ = Opp = 89 Adj Y.
. . Tan42˚ = 89 = Y
Y = 1
Y = x 89
0.89
= m
89 m Ө
Y metres
Angle Ө = 42 degrees

18. TRIGONOMETRY - applications
A four metre length of string, attached to a bolt at the top of a brick wall, makes an angle of 48 degrees with the ground
What is the height (B) of the brick wall? Ө
4 m
B = ?

19. TRIGONOMETRY Draw a diagram Which information do you have?
Sin = Opp/Hyp Cos = Adj/Hyp Tan = Opp/Adj
TRIGONOMETRY
Draw a diagram
Which information do you have?
Which information do you want?
Which function do you use?
Write an equation
Solve the equation
Angle and Hypotenuse
Opposite side, B
Sine
Sin 48 = B/4 Ө
4 m
B = ?
If B = Sin 48 = 0.74 4
B = 0.74 .
. . B = 0.74 X 4
. . B = 2.96 m

20. TRIGONOMETRY

21. TRIGONOMETRY