You are Here: Home >< Maths

# Trigonometry- Half Angle Formulae watch

1. Hi can someone please illustrate to me how to dervive the half angle formulae from the compound angle formulae (or double angle formulae)? thanks
2. sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
let b=a
sin(2a) = sin(a)cos(a) + cos(a)sin(a)
so
sin(2a) = 2sin(a)cos(a)
For the half angle formula. Let 2a = x
sin(x) = 2sin(0.5x)cos(0.5x)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
let b=a
cos(2a) = cos²(a) - sin²(a)
= 2cos²(a) - 1
= 1 - 2sin²(a)
For the half angle formula. Let 2a = x
cos(x) = cos²(0.5x) - sin²(0.5x)
= 2cos²(0.5x) - 1
= 1 - 2sin²(0.5x)
3. (Original post by SsEe)
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
let b=a
sin(2a) = sin(a)cos(a) + cos(a)sin(a)
so
sin(2a) = 2sin(a)cos(a)
For the half angle formula. Let 2a = x
sin(x) = 2sin(0.5x)cos(0.5x)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
let b=a
cos(2a) = cos²(a) - sin²(a)
= 2cos²(a) - 1
= 1 - 2sin²(a)
For the half angle formula. Let 2a = x
cos(x) = cos²(0.5x) - sin²(0.5x)
= 2cos²(0.5x) - 1
= 1 - 2sin²(0.5x)
so which bit do you actually use?

sin(x) = 2sin(0.5x)cos(0.5x)
1 - 2sin²(0.5x)

i understand how you got these, but how do you then use them?
4. Can you just use the double angle formula and divide the answer by 4?
5. What unit is this?
6. (Original post by melbourne)
so which bit do you actually use?

sin(x) = 2sin(0.5x)cos(0.5x)
1 - 2sin²(0.5x)

i understand how you got these, but how do you then use them?
We had a thread about the half-angle formulae a while ago, and decided, I think, by some kind of majority, that you don't really need them.

I can't remember having to use them.

Aitch

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 16, 2005
The home of Results and Clearing

### 1,521

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Bournemouth University
Wed, 22 Aug '18
2. University of Buckingham
Thu, 23 Aug '18
3. University of Glasgow
Tue, 28 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams