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## #1 2005-12-12 08:26:13

Tredici
Member
Registered: 2005-12-12
Posts: 28

### Double/Half Angle Difficulty.

Hey there, I'm not sure where the majority of this community reside, but I'm David and I live in England. I study Maths at A2 Level, (C3). I'm not sure if that's what it's called overseas but I hope it's the same or there's an equivalent.

Anyway, I'm having problems with double and half angle formula application and useage. I've been given a question, and I'd be so undoubtedly greatful if one of you mighty maths minds could work it through for me. Here it is:

Using the identity for cos (A+B), prove that cos θ = 1 - 2 sin² (½θ).

Probably looking at this, you're thinking I'm a complete amateur, but I don't have a clue; I'm stumped. Please help!

Cheers, David.

Last edited by Tredici (2005-12-12 08:35:54)

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## #2 2005-12-12 08:36:27

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Double/Half Angle Difficulty.

cos (A+B) cosAcosB - sinAsinB

Substituting A = B gives cos 2A = cos²A - sin²A

If we then subsitute θ = 2A, we get cosθ = cos² (θ/2) - sin² (θ/2)

Using the identity that cos²θ 1 - sin²θ:

cosθ = 1 - sin²(θ/2) - sin²(θ/2) = 1 - 2sin²(θ/2).

Job done.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2005-12-12 08:47:13

Tredici
Member
Registered: 2005-12-12
Posts: 28

### Re: Double/Half Angle Difficulty.

In the time it took you to do that for me, I had a quick browse around the forum, I don't really know what to say. All I can say is you're all incredibly good at maths, and I really hope you don't mind a not so strong mathematician like myself crashing your parade.

'Mathsyperson', thank you very much. Probably the most annoying thing about maths is once you know the answer getting to it is is a heck of a lot easier. Thanks again my friend!

EDIT: Mathsyperson, are you interested in taking on an apprentice? .

Last edited by Tredici (2005-12-12 08:49:13)

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## #4 2005-12-12 09:02:12

MathsIsFun
Registered: 2005-01-21
Posts: 7,685

### Re: Double/Half Angle Difficulty.

Welcome, Tredici !

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #5 2005-12-12 09:10:07

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Double/Half Angle Difficulty.

What a great thankyou! I'm sure no one minds you 'crashing our parade'. There are loads of people here who never say anything related to maths anyway, so you're actually one of the better people!

And I'm flattered by the offer, but I couldn't possibly take on apprentices for the simple reason that I am not a master.

Why did the vector cross the road?
It wanted to be normal.

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## #6 2005-12-12 11:27:55

justlookingforthemoment
Moderator
Registered: 2005-05-26
Posts: 2,161

### Re: Double/Half Angle Difficulty.

Tredici, you are nowhere near a 'complete amateur'... don't worry! Everyone is welcome, so you don't have to feel like you are barging in.

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## #7 2005-12-12 20:17:10

Flowers4Carlos
Member
Registered: 2005-08-25
Posts: 106

### Re: Double/Half Angle Difficulty.

what is "Maths at A2 Level, (C3)"???

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## #8 2005-12-13 00:27:14

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Double/Half Angle Difficulty.

A2 is the second year of A-levels, and C3 is the 3rd module in the core section of the maths A-level.

Maths A-levels have 4 core modules that everyone does and then 2 modules that you have a choice of. You can do either mechanics (if a ball is dropped off a cliff, how fast is it going when it hits the ground, etc.), statistics (if Timmy throws 5 dice, what's the chance of him scoring 20, etc.) or decision (is it possible to draw a shape without going over lines or taking your pen off the paper, etc.).

Why did the vector cross the road?
It wanted to be normal.

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