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TRIGONOMETRY
Use of Sine, Cosine and
Tangent
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
RATIO = 3
1cm
1.5 cm
Ө
1.12 cm
3 cm
2 cm
4.5 cm
Ө
3 cm
2.24 cm
Ө
3.36 cm
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.
SIMILAR TRIANGLE REVISION
The larger triangles are scaled up versions of the small triangle.
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)
Opposite
Ө
Adjacent
TRIGONOMETRY
Opposite
Ө
Adjacent
TRIGONOMETRY
Opposite
Ө
Adjacent
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
RATIO = 3
1cm
1.5 cm
Ө
1.12 cm
3 cm
2 cm
4.5 cm
Ө
3 cm
2.24 cm
Ө
3.36 cm
TRIGONOMETRY - Sine
The sides within the one (right angled) triangle are related to each other in
ratios which depend on the angle Ө.
Opp = 1 = 2 = 3 = Sine Ө =
Hyp
1.5
3.0
4.5
1cm
0.67
1.5 cm
Ө
1.12 cm
3 cm
2 cm
4.5 cm
Ө
3 cm
2.24 cm
Ө
3.36 cm
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 = 1.12 = 2.24 = 3.36 = Cosine Ө =
Hyp
1.5
3.0
4.5
1cm
0.74
1.5 cm
Ө
1.12 cm
3 cm
2 cm
4.5 cm
Ө
3 cm
2.24 cm
Ө
3.36 cm
TRIGONOMETRY - Sine
For right angled triangles, these ratios have been recorded
and are stored in your calculator
Opp = 2 = 0.67 = Sine Ө = Sin Ө = Sin42˚
Hyp
3
Angle Ө = 42 degrees
3 cm
2 cm
2.24 cm
TRIGONOMETRY - Cosine
Adj =
Hyp
2.24 = 0.74 = Cosine Ө = Cos Ө = Cos42˚
3
Angle Ө = 42 degrees
3 cm
2 cm
2.24 cm
TRIGONOMETRY - Tangent
Opp = 2 = 0.89 = Tangent Ө = Tan Ө = Tan42˚
Adj
2.24
Angle Ө = 42 degrees
3 cm
2 cm
2.24 cm
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)
TRIGONOMETRY
Tan42˚ = Opp
= X
Adj
100
.
. . 0.89 = X
100
.
. . X = 89 metres
Angle Ө = 42 degrees
X metres
(Opposite)
100 metres
(Adjacent)
TRIGONOMETRY
Can you guess what Y could be?
Angle Ө = 42 degrees
89 m
Y metres
TRIGONOMETRY
Can you guess what Y could be?
89 m
Tan42˚ = Opp
= 89
Adj
Y
.
. . Tan42˚ = 89 = 0.89
Y
.
. . Y = 1
89
0.89
.
. . Y = 1 x 89
0.89
= 100 m
Ө
Y metres
Angle Ө = 42 degrees
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?
4m
Ө
B=?
Sin = Opp/Hyp
Cos = Adj/Hyp
TRIGONOMETRY
Tan = Opp/Adj
Draw a diagram
Which information do you have?
Which information do you want?
Which function do you use?
Write an equation Sin 48 = B/4
Solve the equation
If
B = Sin 48 = 0.74
4
B = 0.74
4
Angle and Hypotenuse
Opposite side, B
Sine
4m
.
. . B = 0.74 X 4
.
. . B = 2.96 m
Ө
B=?
TRIGONOMETRY
TRIGONOMETRY