AS Maths Masterclass

Lesson 2:

Trigonometrical equations

Learning objectives

The student should be able to:

• derive standard results for sin, cos, tan of 30, 45 and 60 degrees respectively;

• define the sin, cos and tan functions and sketch their graphs;

• apply the identity when appropriate;

• apply the Pythagorean identity when appropriate.

tancos

sin

1cossin 22

What is trigonometry and where is it used?

It is all about how the sides and angles of a triangle are related to each other.

You are about to see a number of images.

Identify the role played by trigonometry in each case:

The sundial

The speedcam

The pyramids

A map (showing what ?)

A tuning fork

The humble bumble bee

A plug for your electrical gadgets

Every student’s essential kit

A metronome

A spring

Defining the trig functions

You are about to visit an interactive spreadsheet. Notice the colour code for each trig function and the graphs they produce.

Click here to move to the Excel spreadsheet

Key features of sin x graph

• Periodic with period 360 degrees.• Rotational symmetry order 2 about origin.• Vertical lines of symmetry at 90, 270 etc.• Maximum value = 1• Minimum value = -1

Key features of cos x graph

• Periodic with period 360 degrees.• Reflective symmetry in the y axis.• Vertical lines of symmetry at 0, 180, 360 etc.• Maximum value = 1• Minimum value = -1

Key features of tan x graph

• Periodic with period 180 degrees.• Rotational symmetry of order 2.• Vertical lines of symmetry at 0, 180, 360 etc.• Maximum value = • Minimum value = -

Derivation of standard results

Click here for weblink 1: 30, 45, 60 deg.

Click here for the Excel spreadsheet

Click here for the weblink list.