sine and cosine

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Topher
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17 May 2007, 6:49 pm

Can someone tell me how to express 4sin^2x in the forum a+bcos2x complete with workings and where a and b are constants?

thanks

willem
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17 May 2007, 8:47 pm

cos(2x) = cos^2(x) - sin^2(x) =>
sin^2(x) = cos^2(x) - cos(2x) = 1 - sin^2(x) - cos(2x) =>
2sin^2(x) = 1 - cos(2x) =>
4sin^2(x) = 2 - 2cos(2x)
(so a = 2, and b = -2)

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Topher
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18 May 2007, 11:08 am

Thanks dude

Gilb
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18 May 2007, 11:11 am

pfft i think after i have done my A-level i have had enough double angle formula to last a lifetime

matt271
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21 May 2007, 1:41 pm

only one u need to rem is sin^2x+cos^2x=1. the rest come from that. and if u think about that its just parathions theorem where the hypotenuse is 1

nitro2k01
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21 May 2007, 2:20 pm

matt271 wrote:

only one u need to rem is sin^2x+cos^2x=1. the rest come from that.

Yes and no. Strictly speaking what you say is true, but knowing other formulae by heart as well relieves you from having to derive the other every time you want to use them.

matt271 wrote:

and if u think about that its just parathions theorem where the hypotenuse is 1

Don't you mean Pythagoras' theorem?

matt271
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21 May 2007, 4:48 pm

nitro2k01 wrote:

matt271 wrote:

and if u think about that its just parathions theorem where the hypotenuse is 1

Don't you mean Pythagoras' theorem?

thats what spell check corrected it to

nitro2k01
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21 May 2007, 6:34 pm

Hmm, why didn't it try to correct "u" and "rem"?

matt271
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21 May 2007, 6:53 pm

it dont correct letters. a b c d e f g, etc. and rem i dunno, i guess is an accepted shorthand or may be a word for something else.

Saepius
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22 May 2007, 9:06 am

matt271 wrote:

only one u need to rem is sin^2x+cos^2x=1. the rest come from that. and if u think about that its just parathions theorem where the hypotenuse is 1

Heh, I always worked on that principle but it made my Year 12 maths exams hard because I had to work them out each time and not all of them follow in an obvious way.

matt271
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22 May 2007, 4:56 pm

sine is cool, but cosine is an ass!

DrizzleMan
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26 May 2007, 8:16 am

matt271 wrote:

sine is cool, but cosine is an ass!

Differential of ass = -cool?

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matt271
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26 May 2007, 7:28 pm

DrizzleMan wrote:

matt271 wrote:

sine is cool, but cosine is an ass!

Differential of ass = -cool?

and the integral of ass = cool + C
what did we learn here? DONT FORGET TO ADD C!! !! !! !! !! !! !! !! !! !
haa haa haa

DrizzleMan
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28 May 2007, 6:52 am

I C.

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matt271
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28 May 2007, 7:28 am

DrizzleMan wrote:

I C.

nitro2k01
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28 May 2007, 11:06 am

Integrated circuit.

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