Transcript Introduction to Trigonometry

Trigonometry
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S4
Revisited
The Sine Ratio
The Cosine Ratio
The Tangent Ratio
Mixed Problems
Starter Questions
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S4
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Trigonometry
Sine ratio
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S4
Learning Intention
1. Definite the sine ratio and
show how to find a length
or angle using this ratio.
Success Criteria
1. Write down sine ratio.
2. Use sine ratio to find a length
or angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Trigonometry
The Sine Ratio
Sin x° =
Opposite
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x°
Opp
Hyp
Find the
height h
Sine Ratio
Trigonometry
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h
Opp
Opp
Sin x° =
Hyp
Sin 34° =
11cm
34°
h
11
SOH CAH TOA
11 x Sin 34° = h
h = 11 x Sin 34° = 6.2cm (1 d.p.)
Sine Ratio
Find the xo
Trigonometry
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S4
6m
Opp
9m
Opp
Sin x° =
Hyp
6
Sin x° =
9
x°
SOH CAH TOA
Sin x° = 0.667 (3 d.p.)
Sine Ratio
Trigonometry
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S4
Revisited
Sin x° =0.667 (3 d.p.)
How do we find x°?
We need to use Sin ⁻¹on the
calculator.
Sin ⁻¹is written above
To get this press
2nd
Sin ⁻¹
Sin
Followed by
Sin
Sine Ratio
Trigonometry
Revisited
Sin x° = 0.667 (3 d.p.)
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S4
Press
2nd
Enter 0.667
Sin ⁻¹
Sin
=
x = Sin ⁻¹0.667 = 41.8° (1 d.p.)
Sine Ratio
Trigonometry
Revisited
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S4
The support rope is 11.7m long. The angle between
the rope and ground is 70o. Use the sine ratio to
calculate the height of the flag pole.
sin 70o =
opp
h
=
hyp 11.7
SOH CAH TOA
h = 11.7  sin70o
11.7m
h = 11m
16-Jul-15
Compiled by Mr. Lafferty Maths Dept.
70o
h
Sine Ratio
Trigonometry
Revisited
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S4
Use the sine ratio to find the angle of the ramp.
opp 10
sin x =
=
hyp 20
o
SOH CAH TOA
10
sin x =
20
o
 10 
x = sin   = 30o
 20 
o
16-Jul-15
-1
20 m
xo
Compiled by Mr. Lafferty Maths Dept.
10m
Sine Ratio
Trigonometry
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S4
SOH CAH TOA
Opp
Sin x° =
Hyp
Sin 72° =
r=
5
r
5
sin 72o
r = 5.3 km
A road AB is right angled at B.
The road BC is 5 km.
Calculate the length of
the new road AC.
B
5km
C
72°
r
A
Trigonometry
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S4
Sine Ratio
Now try Ex 1 & 2
Ch 13 Page 148
Starter Questions
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S4
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Trigonometry
Cosine Ratio
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S4
Learning Intention
1. Definite the cosine ratio
and show how to find an
length or angle using this
ratio.
Success Criteria
1. Write down cosine ratio.
2. Use cosine ratio to find a
length or angle.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Trigonometry
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S4
Cosine Ratio
Cos x° =
x°
Adjacent
Adj
Hyp
Find the
adjacent
length b
Cosine Ratio
Adj
Cos x° =
Hyp
b
Cos 40° =
35
b
40°
Opp
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Trigonometry
35mm
SOH CAH TOA
35 x Cos 40° = b
b = 35 x Cos 40°= 26.8mm (1 d.p.)
Trigonometry
Cosine Ratio
S4
34cm
Adj
Cos x° =
Hyp
Cos x° =
34
45
Opp
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Find the
angle xo
x°
45cm
SOH CAH TOA
Cos x° = 0.756 (3 d.p.)
x = Cos ⁻¹0.756 =41°
Trigonometry
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Cosine Ratio
Now try Ex 3
Ch 13 Page 153
Starter Questions
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S4
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Angles & Triangles
Learning Intention
1. To use tan of the angle to
solve problems.
Success Criteria
1. Write down tan ratio.
2. Use tan of an angle to solve
problems.
16-Jul-15
Created by Mr. Lafferty Maths Dept.
Trigonometry
Revisited
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S4
How high is the tower?
Opp
60°
12 m
Trigonometry
Revisited
Opposite
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Copy this!
60°
12 m
Adjacent
Trigonometry
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Revisited
Opp
Tan x° =
Adj
Opp
Tan 60° =
12
12 x Tan 60° = Opp
Opp =12 x Tan 60° = 20.8m (1 d.p.)
Copy this!
Trigonometry
Revisited
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S4
So the tower’s
20.8 m high!
20.8m
Don’t worry, you’ll
be trying plenty of
examples!!
Opp
Tan x° =
Adj
Opposite
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General
Trigonometry
x°
Adjacent
Example
Trigonometry
S4
General
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Find the
height h
h
65°
8m
Opp
SOH CAH TOA
Opp
Tan x° =
Adj
Tan 65° =
h
8
8 x Tan 65° = h
h = 8 x Tan 65° = 17.2m (1 d.p.)
Trigonometry
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S4
Revisited
Extension
Booklet
Mixed Ratios
Trigonometry
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Past Paper Type Questions
SOH CAH TOA
The Three Ratios
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adjacent
opposite
Sine
Tangent
Cosine
hypotenuse
adjacent
Sine
adjacent
Cosine
opposite
Cosine
Tangent
Sine
hypotenuse
opposite
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Sine
hypotenuse
Mixed Ratios
Trigonometry
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Sin x° =
Opp
Hyp
Cos x° =
Adj
Hyp
O
A
S HC H
Tan x° =
O
T A
Opp
Adj
Mixed Ratios
Trigonometry
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Process
1.
Write down
SOH CAH TOA
2.
3.
Identify what you want to find
what you know
Copy this!
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
(4 marks)
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
4 marks
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
(4marks)
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
Mixed Ratios
Trigonometry
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S4
Past Paper Type Questions
SOH CAH TOA
(4marks)
Mixed Ratios
Trigonometry
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S4
Now try Ex 4
Ch 13 Page 157