# Double angle formulae

Double angle formulae explained, questions referenced from c3&c4 book

- Created by: Nicola
- Created on: 24-06-10 01:28

First 316 words of the document:

1

W6.1 Double Angle Formulae

In this session, we return to the compound angle formulae from last week.

We'll take the versions which are adding A and B

and we'll replace B with another A.

Let's do it first for sine:

sin(A + B) = sin A cos B + cos A sin B

If we put B = A, this gives:

sin(A + A) = sin A cos A + cos A sin A

or: sin 2A = 2 sin A cos A.

You need to set out to remember this formula

and the other two we shall derive soon.

The next easiest to do is for tangent.

We have: tan (A + B) =

Putting B = A gives us: tan (A + A) =

or: tan 2A =

The cosine double angle formula gives us a bit more fun.

We start with: cos(A + B) = cos A cos B sin A sin B

and put B = A, giving:

cos(A + A) = cos A cos A sin A sin A

or: cos 2A = .........................................(i)

That's the basic cosine double angle formula.

Last year, we learnt the relationship: + = 1 ..............(ii)

which gives us: =1

Use this in (i) to substitute for and you get:

cos 2A = 1 2

If we go back to (ii) and change its subject to ,

substituting that in (i) gives:

cos 2A = 2 1

So there are three versions of the cosine double angle formula

and you need to know all three of them.

NB

The first version of cos2A is in the formula book,

but you have to remember the other two.

[You should, of course, remember all of them!]

Ex

Use sin2A to find sin120°.

If we put A = 60° we have:

CT NHC 22/02/2010

## Comments

No comments have yet been made