- #1

complexhuman

- 22

- 0

How am I meant to derive trig identities like sin(x)cos^3(x) from some complex **** like [tex]\left( {e}^{{\it ix}} \right) ^{n}={e}^{{\it ixn}}[/tex]! I just don't get the idea!

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- Thread starter complexhuman
- Start date

- #1

complexhuman

- 22

- 0

How am I meant to derive trig identities like sin(x)cos^3(x) from some complex **** like [tex]\left( {e}^{{\it ix}} \right) ^{n}={e}^{{\it ixn}}[/tex]! I just don't get the idea!

- #2

inha

- 576

- 1

http://mathworld.wolfram.com/deMoivresIdentity.html

That should get you started. It's all about manipulating the exponential expressions and identifying the trig identities from there.

- #3

lurflurf

Homework Helper

- 2,453

- 149

It might be more clear in the trigonometric form where the equation iscomplexhuman said:

How am I meant to derive trig identities like sin(x)cos^3(x) from some complex **** like [tex]\left( {e}^{{\it ix}} \right) ^{n}={e}^{{\it ixn}}[/tex]! I just don't get the idea!

[cos(x)+i sin(x)]^n=cos(n x)+i sin(n x)

so if you wanted to know

cos(3 x)=[cos(x)]^3-3cos(x)[sin(x)]^2

you could consider

[cos(x)+i sin(x)]^3=cos(3 x)+i sin(3 x)

so expand the left side find its real part and you have the identitiy

the binomial theorem can be helpful here

just be aware that using lots of odd identities at intermediate steps will mess things up

- #4

dx/dy=?

- 49

- 0

thanks for the links inha.

- #5

complexhuman

- 22

- 0

Thanks guys :)

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