Fourier Series of Sin 2x

Hi,

question is to "Write down" the fourier series of sin 2x without resorting to integtation, am I missing something obvious?

thanks

Reply 1

DFranklin

18

Well, is "sin 2x" a Fourier series? And does it equal sin 2x?

Reply 2

Plutoniummatt

OP

8

Im not really that sure, only had 1 lecture on it, and been taught about the methods of finding the Fourier coefficients, but the topic is new to me so I'm not actually sure whats what, can I just write the fourier series of Sin 2x as itself? or by Fourier series do they mean I "have to" express them in terms of an infinite sum?

Reply 3

DFranklin

18

Well, if you write it as

\sum_0^\infty a_k \sin kx

you'll find that a_k = 0 except for when k = 2.

So yeah, just write down "sin 2x".

Reply 4

Plutoniummatt

OP

8

thanks, what about "writing down" the fourier series of (Cos x)^2?

Reply 5

DFranklin

18

Use a trig identity to rewrite it it terms of cos 2x.

Reply 6

astark34

to do it without integration use the complex form of the fourier series. Then use Euler's formula and you can do it without integrating. the answer should be 0 if n does not equal plus or minus 2, 1/2i if n=2, and -1/2i if n=-2

Reply 7

davros

16

Original post by astark34

to do it without integration use the complex form of the fourier series. Then use Euler's formula and you can do it without integrating. the answer should be 0 if n does not equal plus or minus 2, 1/2i if n=2, and -1/2i if n=-2

Why have you just resurrected a thread from five years ago?

(I mean, I know it's Easter but this is ridiculous :smile:

)

Reply 8

Mr M

20

Original post by astark34

to do it without integration use the complex form of the fourier series. Then use Euler's formula and you can do it without integrating. the answer should be 0 if n does not equal plus or minus 2, 1/2i if n=2, and -1/2i if n=-2