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

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1. Trigonometry 1

Foundation Year Program
NUFYP Mathematics
Trigonometry 1
Rida El-Mehdawe
2019-2020

2.

Foundation Year Program
What does π
mean?
Trigonometry 1
Arc length
Sector area
Right triangle ratios
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3. Introduction

Foundation Year Program
Introduction
Some application of trigonometry.
Construction tools, and windshield
Wiper.
Is it useful to relate logarithm to trigonometry? YES
simplification of reducing multiplication and division
to addition and subtraction. How?
Taking the log of both sides of the law of sine(Will
be studied in 3.5).
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4. Basic definitions

Foundation
Foundation Year
Year Program
Basic definitions
• If the arc AB has length

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