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

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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

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x°x°

Sin x° =

Opp

Opp

Hyp

Hyp6m6m 9m9m

Sin x° =

69

= 0.667 (3 d.p.)

Sin x°

Find the xo

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Sine Ratio

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=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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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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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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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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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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Now try Ex 1 & 2

Ch 13 Page 148

Sine RatioS4



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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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Cos x° =

Adjacent

Adj

x°x°

Hyp

hypotenuse

Cosine RatioS4

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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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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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Now try Ex 3

Ch 13 Page 153

Cosine RatioS4



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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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12 m

How high is the tower?

Opp

60°

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60°

12 mAdjacent

Op

posit

e

hypotenuse Copy this!

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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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So the tower’s 20.8 m high!

Don’t worry, you’ll be trying plenty of examples!!

20.8m

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Adj

x°x°

Tan x° =O

pp

osit

e

Opp

Adjacent

S4 General

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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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ExtensionBooklet

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TrigonomeTrigonometrytryPast Paper Type Questions

SOH CAH TOA

Mixed Ratios

S4


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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Sin x° =Opp

HypCos x° =

Adj

HypTan x° =

Opp

Adj

CAH TOASOH

Mixed Ratios

S4

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SOH CAH TOA

Copy this!

1. Write down

Process

Identify what you want to find

what you know3.

2.

Mixed Ratios

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(4 marks)

SOH CAH TOA

Mixed Ratios

S4

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SOH CAH TOA

Mixed Ratios

S4

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SOH CAH TOA

4 marks

Mixed Ratios

S4

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S4

SOH CAH TOA

Mixed Ratios

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TrigonomeTrigonometrytryPast Paper Type QuestionsS4

(4marks)

SOH CAH TOA

Mixed Ratios

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SOH CAH TOA

Mixed Ratios

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(4marks)

SOH CAH TOA

Mixed Ratios

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Now try Ex 4

Ch 13 Page 157

Mixed Ratios

S4

Www.mathsrevision.com Trigonometry S4 Revisited The Sine Ratio The Cosine Ratio Mixed Problems The...

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