Trigonometry

10

11.1 Introduction

EMCCE

In this chapter we will build on the trigonometryfrom previous years by looking at the result applying

trigonometric functionsto sums and differencesof angles. We will alsoapply trigonometry to solving

geometric problems in two and three dimensions.

See introductory video:VMhtu at http://www.everythingmaths.co.za

10.2 Compound AngleIdentities EMCCF

Derivation ofsin(α+β) EMCCG

We have, for any angles α and β, that

sin(α +β) = sinα cosβ + sinβ cosα

How do we derive this identity? It is tricky, so follow closely.

Suppose we have the unit circle shown below. The two points L(a;b) and K(x;y) are on the circle.