Trigonometry National 4 REL 1.3a REL 1.3b Investigating the Tangent Ratio The Sine Ratio (Finding a...

srevis

TrigonomeTrigonometrytry

National 4 REL 1.3a REL 1.3b

Investigating the Tangent Ratio

The Sine Ratio (Finding a length)

The Sine Ratio (Finding an angle)

The Cosine of an Angle

Mixed Problems

The Tangent (Finding lengths)

The Tangent (Finding the Angle)

The Cosine ( Finding a length)

Starter QuestionsStarter Questions

18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

srevis

266 % of £ 270

3Q1. Calculate

Q2. Convert 60% to fraction and simplify.

Q3. Convert

Q4. What is the time difference 09:28 and 10:50

to a percentage.

Q5. The answer to the question is 90. What is thequestion.

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

srevis

.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria

2.2. Work out Tan Ratio.Work out Tan Ratio.

1. To identify the hypotenuse, opposite and adjacent sides in a right angled triangle.

Angles & Angles & Triangles Triangles

1.1. Understand the terms Understand the terms hypotenuse, opposite and hypotenuse, opposite and adjacent in right angled adjacent in right angled triangle.triangle.

srevis

Trigonometry means “triangle” and “measurement”.

AdjacentO

x°x°

hypotenuse

We will be using right-angled triangles.

These triangles have 2 things in common

One is 37o

The other we will investigate

Triangle A B C D

Vertical side 3cm 6cm 4cm

Horizontal side 4cm 8cm 6cmVertical

Horizontal

1.5cm2cm

0.75 0.75

www.mathsrevision.comwww.mathsrevision.com

srevis

.com For the RAT with angle of 37o

the answer obtained by dividing vertical side by horizontal side was

Right-Angled Triangle

ALWAYS 0.75

The number has a special name

It is called the TANGENT of 37o

tan37o

srevis

Using a calculator to find tan ratio What Goes In The Box ?

Find the tan ratio to 3 decimal places.

tan 30o tan 0o tan 45o

tan 60o tan 20o tan 70o

= 0.577

= 0.000

= 1.000

= 1.732

= 0.364

= 2.747

srevis

x°x°

Tan x° =O

Adjacent

srevis

12 mAdjacent

hypotenuse Copy this!

srevis

Tan x° =

Tan 60° =

12 x Tan 60°Opp =

12 x Tan 60°= 20.8m (1 d.p.)

Copy this!

srevis

Tan Ratio Ex1

Ch16 Page 198

www.mathsrevision.comwww.mathsrevision.comww

srevis

.com 1. True or f alse 30 5 + 6 4 = 48

2. Write in scientifi c notation 0.0456

3. I dentif y the sides of the triangle.

4. A train takes 6 hrs to travel 360 miles apart.

Calculate it's average speed.

srevis

2.2. Use tan of an angle to Use tan of an angle to solve REAL LIFE problems.solve REAL LIFE problems.

1. To use tan of the angle to solve REAL LIFE problems.

1.1. Write down tan ratio.Write down tan ratio.

srevis

x°x°

Tan x° =O

Adjacent

srevis

Example Example

65°65°

Tan x° =

OppOpp

Hyp hh

8m8m Tan 65° =

8 x Tan 65°

8 x Tan 65° = 17.2m (1 d.p.)

National 4 REL 1.3 a + 1.3b

Find the height h

SOH CAH TOA

srevis

SOH CAH TOA

18 Apr 202318 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.

Use the tan ratio to find the height h of the tree

to 2 decimal places.

o opp htan 47 = =

o htan 47 =

oh = 8 × tan 47

h = 8.58m

srevis

18 Apr 2023Compiled by Mr. Lafferty Maths

Aeroplane

a = 15

Lennoxtown

Airport

Q1.Q1. An aeroplane is preparing to land at Glasgow An aeroplane is preparing to land at Glasgow Airport. Airport. It is over Lennoxtown at present which is It is over Lennoxtown at present which is 15km from 15km from the airport. The angle of descent is 6the airport. The angle of descent is 6oo. .

What is the height of the plane ?What is the height of the plane ?

Example 2Example 2

o htan 6 =

oh = 15 × tan 6

h = 1.58km

SOH CAH TOA

srevis

Use the tan ratio to calculate how far the ladder is away from the building.

ladder

o opp 12tan 45 = =

tan 45

d = 12m

SOH CAH TOA

srevis

Aeroplane

a = 1.58 km

Lennoxtown

Airport

Q1. An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present. It is at a height of 1.58 km above the ground. It ‘s angle of descent is 6o.

How far is it from the airport to Lennoxtown?

Example 2Example 2

o 1.58tan 6 =

1.58d =

d = 15 km

SOH CAH TOA

srevis

Now tryExercise 2

Ch16 (page 199)

srevis

.com 1. Find the area and perimeter

of the circle.

2. I s the triangle right -angled at P. Explain your answer.

srevis

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.

1.1. Write down tan ratio.Write down tan ratio.

Using Tan to calculate anglesUsing Tan to calculate angles

srevis

Using a calculator to find anglegiven tan ratio

What Goes In The Box ?

Find the angle given the tan ratio to 1 decimal places.

tan-1 1 tan-1 0.5 tan-1 0.8

tan-1 0.6 tan-1 2 tan-1 3

= 45.0o = 26.6o

= 38.7o

= 31.0o = 64.4o = 71.6o

srevis

ExampleExample

x°Tan x° =

OppOpp

SOH CAH TOA

12m Tan x° =

= 1.5 Tan x°

Calculate the tan xo

srevis

= 1.5Tan x°How do we find x°?

We need to use Tan ⁻¹on the calculator.

Tan ⁻¹is written above Tan

Tan ⁻¹

To get this press TanFollowed by

Calculate the size of angle xo

srevis

Tan ⁻¹1.5 = 56.3° (1 d.p.)

= 1.5Tan x°

2nd Tan

Tan ⁻¹

Enter =1.5

srevis

Process

1. Identify Hyp, Opp and Adj

2. Write down ratio Tan xo = Opp Adj

3. Calculate xo 2nd Tan

Tan ⁻¹

srevis

Use the tan ratio to calculate the angle that the support wire makes with the ground.

o opp 11tan x = =

o -1x = tan

o ox = 70

SOH CAH TOA

srevis

Now tryExercise 3

Ch16 Page 202

18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

srevis

.com 4 13 11 3

2. The ratio of apples to pears is 2:5.

I f there are 28 pieces of f ruit in total.

How many apples are there.

a a d a a d 1. Simplify

3. Find HCF of 8 and 18

srevis

2.2. Use sine ratio to find an Use sine ratio to find an angle.angle.

1. Definite the sine ratio and show how to find an angle using this ratio.

1.1. Write down sine ratio.Write down sine ratio.

srevis

TrigonomeTrigonometrytryThe Sine RatioThe Sine Ratio

x°x°

Sin x° =O

OppHyp

hypotenuse

srevis

Using a calculator to find sin ratio What Goes In The Box ?

Find the sin ratio to 3 decimal places.

sin 30o sin 0o sin 45o

sin 60o sin 20o sin 90o

= 0.500

= 0.000

= 0.707

= 0.866

= 0.342

= 1.000

srevis

ExampleExample

34°34°Sin x° =

OppOpp

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

srevis

SOH CAH TOA

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.

o opp hsin 70 = =

hyp 11.7

h o= 11.7 sin70

h = 11 m

srevis

SOH CAH TOA

ExampleExample

72°72°

Sin x° =Opp

Sin 72° =

5.3 km

5km5km

r5sin72o

A road AB is right angled at B. The road BC is 5 km.

Calculate the length of the new road AC.

srevis

Now tryExtension Booklet

Ex4E (page 83)

srevis

1. Calculate the mean median and mode f or the data below 19, 15, 11, 22, 9, 12, 11

2. The price of a car is £ 9000

I t is reduced by 20% in a sale.

What is the price of the car now?

3. A lorry is travelling at 40mph.

I t has travelled 60 miles. How long has it taken to travel 60 miles.

srevis

2.2. Use sine ratio to find angle Use sine ratio to find angle REAL-LIFE problems.REAL-LIFE problems.

1. To show how to use the sine ratio to find angle in REAL-LIFE problems.

1.1. Write down sine ratio.Write down sine ratio.

Using Sin to calculate anglesUsing Sin to calculate angles

srevis

Using a calculator to find anglegiven sin ratio

Find the angle given the sin ratio to 1 decimal places.

sin-1 1 sin-1 0.5 sin-1 0.8

sin-1 0.6 sin-1 0.1 sin-1 0.9

= 90.0o = 30.0o

= 53.1o

= 36.9o = 5.7o = 64.2o

srevis

ExampleExample

x°x°

Sin x° =

Hyp6m6m 9m9m

Sin x° =

= 0.667 (3 d.p.)

Sin x°

Find the xo

SOH CAH TOA

srevis

=0.667 (3 d.p.)Sin x°How do we find x°?

We need to use Sin ⁻¹on the calculator.

Sin ⁻¹is written above Sin

Sin ⁻¹

To get this press SinFollowed by

srevis

Sin ⁻¹0.667 = 41.8° (1 d.p.)

= 0.667 (3 d.p.)

Sin x°

2nd Sin

Sin ⁻¹

Enter =0.667

srevis

SOH CAH TOA

Use the sine ratio to find the angle of the ramp.

o opp 10sin x = =

hyp 20

o 10sin x =

o -1 o10x = sin = 30

srevis

Ex5E (page 85)

srevis

1. Calculate the mean median and mode f or the data below 9, 5, 11, 2, 9, 2

2. The price of a f ootball is £ 20.

I t is reduced in a sale by 80%.

What is the sale price.

3. A lorry is travelling at 50mph.

I t has travelled 75 miles.

srevis

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.

1.1. Write down cosine ratio.Write down cosine ratio.

srevis

Using a calculator to find cos ratio What Goes In The Box ?

Find the cos ratio to 3 decimal places.

cos 30o cos 0o cos 45o

cos 60o cos 20o cos 90o

= 0.866

= 1.000

= 0.707

= 0.500

= 0.940

= 0.000

srevis

The Cosine The Cosine RatioRatio

Cos x° =

Adjacent

x°x°

hypotenuse

srevis

SOH CAH TOA

ExampleExample

40°40°Cos x° =

Hyp Hyp

Cos 40° =

35 x Cos 40°

= 26.8mm (1 d.p.)

Find the adjacent length b

srevis

Now tryExtension BookletEx6E (page 88 Q1 to

18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

Starter QuestionsStarter Questionsw

srevis

5 6 7 3 3

2. The ratio of apples to pears is 4:5.

I f there are 72 pieces of f ruit in total.

How many apples are there.

y x x x xy 1. Simplify

3. Find HCF of 15 and 21

srevis

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.

1.1. Write down cosine ratio.Write down cosine ratio.

Using Cos to calculate anglesUsing Cos to calculate angles

srevis

Using a calculator to find anglegiven cos ratio

Find the angle given the cos ratio to 1 decimal places.

cos-1 1 cos-1 0 cos-1 0.8

cos-1 0.6 cos-1 0.1 cos-1 0.9

= 0.0o = 90.0o

= 36.9o

= 53.1o = 84.3o = 25.8o

srevis

SOH CAH TOA

ExampleExample

x°x°Cos x° =

Hyp Hyp45cm

Cos x° = 3445= 0.756 (3 d.p.)Cos

x°x =

Cos ⁻¹0.756 =41°

Adj34cm34cm

Find the angle xo

srevis

Now tryExtension BookletEx6E (page 89 Q6 to

srevis

1. Calculate 104 x 100

putting your answer in standard f orm.

2. I s this triangle right angled ?

I f yes, fi nd the size of angle x .

I f no fi nd the area of the triangle.

The Three RatiosThe Three Ratios

Cosine

Tangent

Cosine

srevis

opposite

opposite opposite

adjacent

hypotenuse

srevis

Sin x° =Opp

HypCos x° =

HypTan x° =

CAH TOASOH

srevis

SOH CAH TOA

Copy this!

1. Write down

Process

Identify what you want to find

what you know3.

srevis

TrigonomeTrigonometrytryPast Paper Type Questions

SOH CAH TOA

srevis

(4 marks)

SOH CAH TOA

srevis

SOH CAH TOA

srevis

SOH CAH TOA

4 marks

srevis

SOH CAH TOA

srevis

(4marks)

SOH CAH TOA

srevis

SOH CAH TOA

srevis

(4marks)

SOH CAH TOA

srevis

Ex7E (page 91)

Trigonometry National 4 REL 1.3a REL 1.3b Investigating the Tangent Ratio The Sine Ratio (Finding a...

Documents

3-3 The Sine and Cosine Ratio · 2019. 5. 15. · Math 10 Ch 3. Right Triangle Trigonometry Lesson 3-3 Lesson 3-3: The Sine and Cosine Ratio Did you ever wonder where does the word

Sine Wave Filter - MTE Corporation · 2020. 10. 11. · 1. IMPORTANT SAFETY INFORMATION 1 Part No. INSTR-020 REL. 041116 WARNING ONLY A QUALIFIED ELECTRICIAN CAN CARRY OUT THE ELECTRICAL

sine function

3.2 The Sine and Cosine Ratios - Weeblymrsduprey.weebly.com/uploads/2/3/4/1/23411986/m10ch03_3...ratios, called the sine ratio and cosine ratio, involve the hypotenuse. Investigate

Right Triangle Trigonometry · cause the ball to travel different distances and different heights. One design element of a golf club is the angle of the club face. Sine Ratio Sine

Home - Education Bureau - S2 Mathematics...the ratio of the opposite side of ϴto the hypotenuse is a constant. We call this ratio the sine ratio of ϴ… What? Why? How? the hypotenuse

Chapter 1 - Introduction - Spectral Dynamics · 2017-05-18 · Sine on Random Operating M anual 2400 -0133 BETA REL EASE Chapter 1 - Introduction 1.1 Introduction This manual describes

Trigonometry S3 Credit The Tangent Ratio The Tangent using Angle The Sine of an Angle The Sine Ration In Action The Cosine of an

Sine Inverter

HSPA+ LTE Carrier Aggregation - telecomwebinar.com · Nokia Siemens Networks Presented by: Erasmo Rojas, 4G Americas ... DC-HSUPA Y Rel-7 Rel-8 Rel-9 Rel-10 Rel-11 Rel-12 LTE Single

Sine Curve

Rel 8.3 Primavera Fundamentals Rel 8

sine bar Sine bar YEAR/METROLOG… · · 2017-09-30Principle of Sine bar . Accuracy requirements of sine bar: The accuracy of sine bar depends on the following constructional features:

smart 2 6.notebook - Weebly · 2018. 10. 10. · smart_2_6.notebook Homework: pg 112, #816 Athe tangent ratio Bthe sine ratio 1 Û (For another question, go to the next page.) Cthe

02 Overview Rel-6 and Rel-7 Features

Law of Sines Law of Cosine. Law of Sines The ratio of the Sine of one angle and the length of the side opposite is equivalent to the ratio of the Sine

Sine Ratio

sine Toxins

Trigonometry Let’s Investigate Extension The Tangent Ratio The Tangent Angle The Sine Ratio The Sine Angle The Cosine Ratio The

The Tangent Ratio The Tangent using Angle The Sine of an Angle The Sine Ration In Action The Cosine of an Angle Mixed Problems The Tangent Ratio in Action