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August 6th, 2013, 04:25 AM   #1
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Express cos(4a) + sin(4a) using only cos(a) and sin(a)

Hello,


Distribute and group terms containing i:


1. Now, just by seeing a glaring pattern, I am almost convinced that and , but how can I be sure?
2. What is the name of the "method" used to arrive at the above conclusion? (I am sorry that I do not know a more precise word than 'method'.)

Thank you for your time.

Kind regards,
Marius
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August 6th, 2013, 01:01 PM   #2
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Re: Express cos(4a) + sin(4a) using only cos(a) and sin(a)

1. When you have an equation involving complex quantities, the real and imaginary parts are separate equations.
2. I don't know if it has a specific name.

Question - title seems to have little relation to the text.
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September 6th, 2013, 01:48 AM   #3
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Re: Express cos(4a) + sin(4a) using only cos(a) and sin(a)

Hi
solved your problem here
"Solution: Given cos (3?) + i sin (3?) = (cos ? + i sin ?)^3
we know by de Moivre's theorem (cos ? + i sin ?)^n = cos (n?) + i sin (n?)
where cos (3?) = cos^3 ? - 3cos ? sin² ?
sin (3?) = 3cos² ? - sin ^3 ? "
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September 6th, 2013, 12:09 PM   #4
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Similarly, cos(4a) + sin(4a) ? 1 + 4sin(a)cos³a - 8sin²a cos²a - 4sin³a cos(a).
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