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Transcript of Www.mathsrevision.com Trigonometry S4 Revisited The Sine Ratio The Cosine Ratio Mixed Problems The...
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TrigonomeTrigonometrytryS4 RevisitedRevisited
The Sine Ratio
The Cosine Ratio
Mixed Problems
The Tangent Ratio
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Starter QuestionsStarter Questionsw
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S4
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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2.2. Use sine ratio to find a Use sine ratio to find a length or angle.length or angle.
1. Definite the sine ratio and show how to find a length or angle using this ratio.
TrigonometryTrigonometry
1.1. Write down sine ratio.Write down sine ratio.
Sine ratioS4
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TrigonomeTrigonometrytryThe Sine RatioThe Sine Ratio
x°x°
Sin x° =O
pp
osit
e
OppHyp
hypotenuse
S4
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TrigonomeTrigonometrytry
34°34°Sin x° =
OppOpp
Hyp
Hyphh
11c11cmm
Sin 34° =
h11= h11 x Sin
34°h = 11 x Sin
34°= 6.2cm (1 d.p.)
Find the height h
SOH CAH TOA
Sine Ratio
S4
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TrigonomeTrigonometrytry
x°x°
Sin x° =
Opp
Opp
Hyp
Hyp6m6m 9m9m
Sin x° =
69
= 0.667 (3 d.p.)
Sin x°
Find the xo
SOH CAH TOA
Sine Ratio
S4
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TrigonomeTrigonometrytryS4 RevisitedRevisited
=0.667 (3 d.p.)Sin x°How do we find x°?
We need to use Sin ⁻¹on the calculator.
2nd
Sin ⁻¹is written above Sin
Sin ⁻¹
To get this press SinFollowed by
Sine Ratio
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TrigonomeTrigonometrytryS4 RevisitedRevisited
x =
Sin ⁻¹0.667 = 41.8° (1 d.p.)
= 0.667 (3 d.p.)
Sin x°
2nd Sin
Sin ⁻¹
Press
Enter =0.667
Sine Ratio
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TrigonomeTrigonometrytryS4 RevisitedRevisited
SOH CAH TOA
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
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.
70o
h
o opp hsin 70 = =
hyp 11.7
h o= 11.7 sin70
h = 11 m
11.7m
Sine Ratio
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TrigonomeTrigonometrytryS4 RevisitedRevisited
SOH CAH TOA
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Use the sine ratio to find the angle of the ramp.
xo10m
o opp 10sin x = =
hyp 20
o 10sin x =
20
o -1 o10x = sin = 30
20
20 m
Sine Ratio
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TrigonomeTrigonometrytry
SOH CAH TOA
72°72°
Sin x° =Opp
Hyp
Sin 72° =
5r
r =
r =
5.3 km
5km5km
AB
C
r5sin72o
A road AB is right angled at B. The road BC is 5 km.
Calculate the length of the new road AC.
Sine Ratio
S4
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TrigonomeTrigonometrytry
Now try Ex 1 & 2
Ch 13 Page 148
Sine RatioS4
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S4
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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2.2. Use cosine ratio to find a Use cosine ratio to find a length or angle.length or angle.
1. Definite the cosine ratio and show how to find an length or angle using this ratio.
TrigonometryTrigonometry
1.1. Write down cosine ratio.Write down cosine ratio.
Cosine RatioS4
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TrigonomeTrigonometrytry
Cos x° =
Adjacent
Adj
x°x°
Hyp
hypotenuse
Cosine RatioS4
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TrigonomeTrigonometrytry
SOH CAH TOA
40°40°Cos x° =
Opp
Adj
Hyp Hyp
b
35mm
Cos 40° =
b35
= b
35 x Cos 40°
b =
35 x Cos 40°
= 26.8mm (1 d.p.)
Adj
Find the adjacent length b
Cosine RatioS4
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TrigonomeTrigonometrytry
SOH CAH TOA
x°x°Cos x° =
Opp
Adj
Hyp Hyp45cm
Cos x° = 3445= 0.756 (3 d.p.)Cos
x°x =
Cos ⁻¹0.756 =41°
Adj34cm34cm
S4
Find the angle xo
Cosine Ratio
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TrigonomeTrigonometrytry
Now try Ex 3
Ch 13 Page 153
Cosine RatioS4
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S4
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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2.2. Use tan of an angle to Use tan of an angle to solve problems.solve problems.
1. To use tan of the angle to solve problems.
Angles & Angles & Triangles Triangles
1.1. Write down tan ratio.Write down tan ratio.
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TrigonomeTrigonometrytryS4 RevisitedRevisited
12 m
How high is the tower?
Opp
60°
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TrigonomeTrigonometrytryS4 RevisitedRevisited
60°
12 mAdjacent
Op
posit
e
hypotenuse Copy this!
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TrigonomeTrigonometrytryS4 RevisitedRevisited
Tan x° =
Opp
Adj
Tan 60° =
Opp12
= Opp
12 x Tan 60°Opp =
12 x Tan 60°= 20.8m (1 d.p.)
Copy this!
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TrigonomeTrigonometrytryS4 RevisitedRevisited
So the tower’s 20.8 m high!
Don’t worry, you’ll be trying plenty of examples!!
20.8m
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TrigonomeTrigonometrytry
Adj
x°x°
Tan x° =O
pp
osit
e
Opp
Adjacent
S4 General
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TrigonomeTrigonometrytry
Example Example
65°65°
Tan x° =
OppOpp
Adj
Hyp hh
8m8m Tan 65° =
h8
= h
8 x Tan 65°
h =
8 x Tan 65° = 17.2m (1 d.p.)
Adj
S4 General
Find the height h
SOH CAH TOA
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TrigonomeTrigonometrytryS4 RevisitedRevisited
ExtensionBooklet
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TrigonomeTrigonometrytryPast Paper Type Questions
SOH CAH TOA
Mixed Ratios
S4
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The Three RatiosThe Three Ratios
Cosine
Sine
Tangent
Sine
Sine
Tangent
Cosine
Cosine
Sine
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opposite
opposite opposite
adjacent
adjacent
adjacent
hypotenuse
hypotenuse
hypotenuse
S4
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TrigonomeTrigonometrytry
Sin x° =Opp
HypCos x° =
Adj
HypTan x° =
Opp
Adj
CAH TOASOH
Mixed Ratios
S4
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TrigonomeTrigonometrytry
SOH CAH TOA
Copy this!
1. Write down
Process
Identify what you want to find
what you know3.
2.
Mixed Ratios
S4
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TrigonomeTrigonometrytryPast Paper Type Questions
(4 marks)
SOH CAH TOA
Mixed Ratios
S4
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TrigonomeTrigonometrytryPast Paper Type Questions
SOH CAH TOA
Mixed Ratios
S4
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TrigonomeTrigonometrytryPast Paper Type Questions
SOH CAH TOA
4 marks
Mixed Ratios
S4
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TrigonomeTrigonometrytryPast Paper Type Questions
S4
SOH CAH TOA
Mixed Ratios
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TrigonomeTrigonometrytryPast Paper Type QuestionsS4
(4marks)
SOH CAH TOA
Mixed Ratios
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TrigonomeTrigonometrytryPast Paper Type QuestionsS4
SOH CAH TOA
Mixed Ratios
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TrigonomeTrigonometrytryPast Paper Type QuestionsS4
(4marks)
SOH CAH TOA
Mixed Ratios
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TrigonomeTrigonometrytry
Now try Ex 4
Ch 13 Page 157
Mixed Ratios
S4