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#1 2010-05-10 17:59:50

mickeen
Member
Registered: 2009-04-18
Posts: 10

Trigonometry

(a) Express Sin2A + Sin2B as a product in Sine and Cosine.

(b) If A + B + C = 180 degrees,
      show that Sin (A + B) = Sin C

(c) Hence show that Sin 2A + Sin 2B _ Sin 2C = 4CosACosBSinC.

     Note: Cos(A + B) = - CosC

Can anyone plese help me on the last part of this question which has bothered me for some time now.

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#2 2010-05-10 18:04:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,388

Re: Trigonometry

Hi mickeen;

a) First thing that comes to mind is:

b) If A + B + C = 180 then A + B = 180 - C and 

sin( 180 - c ) = sin(180° )cos(c) - cos(180° )sin(c)

= sin(c)

For c)

(c) Hence show that Sin 2A + Sin 2B _ Sin 2C = 4CosACosBSinC.

What does the underscore mean?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2010-05-10 18:34:45

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Trigonometry

(a) Express Sin2A + Sin2B as a product in Sine and Cosine.

Last edited by ZHero (2010-05-10 20:08:26)


If two or more thoughts intersect with each other, then there has to be a point.

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#4 2010-05-10 19:28:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,388

Re: Trigonometry

Hi mickeen;

For C)

Sin 2A + Sin 2B _ Sin 2C = 4CosACosBSinC.

I going to assume you meant:

remember sin(C) = sin(A+B)

See the result I gave you in post #6, Use it right here.

Done!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2010-05-10 20:09:00

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Trigonometry

(b) If A + B + C = 180 degrees,
      show that Sin (A + B) = Sin C


If two or more thoughts intersect with each other, then there has to be a point.

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#6 2010-05-10 20:26:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,388

Re: Trigonometry

Hi mickeen;

For a) this came to me while doing c)

http://www.sosmath.com/trig/Trig5/trig5/trig5.html

The sum to product formulas:

Just say u = 2A and v = 2B

And you get:


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2010-05-15 06:52:02

mickeen
Member
Registered: 2009-04-18
Posts: 10

Re: Trigonometry

Thanks a million for this. I have printed it off and will try to digest it over a bowl of soup and a glass of wine later tonight!

mickeen

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#8 2010-05-15 06:53:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,388

Re: Trigonometry

Hi mickeen;

Enjoyed working on c), thanks for posting it. Save me some soup.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#9 2010-05-17 08:46:10

mickeen
Member
Registered: 2009-04-18
Posts: 10

Re: Trigonometry

Bobby M,

thanks for your help again this time! Dont know what I would do without you! I have it all written out now again (your explanation) and understand it perfectly. Are you any good on Stats? I am OK a while but might have a few questions in June. The soup and the wine was nice. But all gone by the end of the 80 mile cycle yesterday morning! I suppose one cant really share cyber soup! However! Thanks again!

Mickeen

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#10 2010-05-17 08:51:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,388

Re: Trigonometry

Hi mickeen;

You mean I got some of that right!!!!! I knew those Tarot cards worked.

Thanks man. I am glad you got it. I can do some stats and I like it. I am unusually good in stats, getting half of the questions right, provided it is a 2 choice per question test. I know what you would do without me, better! Bring it in and if I am around I will help. Don't worry about the soup.

Just let me say, thanks for saying those kind things, lately I have been feeling pretty unappreciated by some people.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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