Trigonometry 1

Introduction

Basic definitions

Converting angles Example 1

Example 2

Example 3 Find the length of the arc of a circle of radius 5.2 cm, given that the arc subtends an angle of 0.8 rad at the

Example 4. if the arc length (l) of a circle with a radius r is 5 cm, and θ subtends that arc. a. solve for θ b. solve for r

Example 5. A measuring wheel with a radius of 25cm is used to measure a 30m distance. Calculate the angle in Rad, and the

Example 5. A measuring wheel with a radius of 25cm is used to measure a 30m distance. How many revolutions it has to do? Is any

3.1.1 Area of a sector

Example 6 A plot of land is in the shape of a sector of a circle of radius 55 m. The length of fencing that is erected along

Your turn

Your turn

Solution

3.1.2 Basic trigonometric functions

Example 8 Draw diagrams to show the position of OP where θ=〖400〗^o .

Your turn! Draw diagrams to show the position of OP where θ=〖-480〗^o .

Example 9 Write down the values of sin⁡〖〖90〗^o 〗 and cos 180^o.

Some values of trig rations you should know

Proof for angles 30o, and 60o

Proof for angle 45o

Example 10.

Applications,

Your turn!

Your turn!

Area of a triangle

Example 10

Your turn

Why?

Learning outcomes

Formulae

Preview activity: Trigonometry 2

Trigonometry 1

Introduction

Basic definitions

Converting angles Example 1

Example 2

Example 3 Find the length of the arc of a circle of radius 5.2 cm, given that the arc subtends an angle of 0.8 rad at the

Example 4. if the arc length (l) of a circle with a radius r is 5 cm, and θ subtends that arc. a. solve for θ b. solve for r

Example 5. A measuring wheel with a radius of 25cm is used to measure a 30m distance. Calculate the angle in Rad, and the

Example 5. A measuring wheel with a radius of 25cm is used to measure a 30m distance. How many revolutions it has to do? Is any

3.1.1 Area of a sector

Example 6 A plot of land is in the shape of a sector of a circle of radius 55 m. The length of fencing that is erected along

Your turn

Your turn

Solution

3.1.2 Basic trigonometric functions

Example 8 Draw diagrams to show the position of OP where θ=〖400〗^o .

Your turn! Draw diagrams to show the position of OP where θ=〖-480〗^o .

Example 9 Write down the values of sin⁡〖〖90〗^o 〗 and cos 180^o.

Some values of trig rations you should know

Proof for angles 30o, and 60o

Proof for angle 45o

Example 10.

Applications,

Your turn!

Your turn!

Area of a triangle

Example 10

Your turn

Why?

Learning outcomes

Formulae

Preview activity: Trigonometry 2

1.66M

Category: $mathematics$ mathematics

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1. Trigonometry 1

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Trigonometry 1
Rida El-Mehdawe
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2.

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Arc length
Sector area
Right triangle ratios
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3. Introduction

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simplification of reducing multiplication and division
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Taking the log of both sides of the law of sine(Will
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4. Basic definitions

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Basic definitions
• If the arc AB has length

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