6

Trigonometry

Trigonometry (literally: ‘the measurement of triangles’ – ‘trig’ from now on) is a fairly
straightforward topic conceptually, but there always seems a lot to remember. In fact you
only have to remember a few key results – but you have to remember them very well. For
example look at the function

cos 2θ

cosθ+sinθ

If you have to consult a formula book to remind yourself that cos 2θ=cos^2 θ−sin^2 θand
the difference of squares identitya^2 −b^2 =(a−b)(a+b)then it might not even occur
to you to simplify this to the form

cos^2 θ−sin^2 θ

cosθ+sinθ

=

(cosθ−sinθ)(cosθ+sinθ)

cosθ+sinθ

=cosθ−sinθ

However, there is no need to remember the double angle formulae in detail because you can
get them easily from the compound angle formulae for cosine and sine, which youshould
remember well. In this chapter we will cover such fundamental topics of trigonometry,
and encourage you to learn just a few key formulae very well so that you can use these
to derive other formulae as you need them.

Prerequisites

It will be helpful if you know something about:

• angular measurement using degrees and radians (148

➤

)

• ratio and proportion (14

➤

)

• properties of triangles (150
  ➤
  )


• Pythagoras’ theorem (154
  ➤
  )


• plotting graphs (91
  ➤
  )


• inverse of a function (100
  ➤
  )


• surds (20
  ➤
  )

Objectives

In this chapter you will find:

• radian measure and the circle


• definitions of the trig ratios