Finding the coeffiecients of a sine series for -3*cos(8*pi*x/L)

[dnp33]

Homework Statement

all i really need to do is solve the integral:
$$\int-3*sin(\frac{n*pi*x}{L})*cos(\frac{8*pi*x}{L})$$
from x=0 to x=L

Homework Equations

The Attempt at a Solution

I'm not very sure where to start with this. Any help would be appreciated.

 

[Gib Z]

Seeing as you are finding a Fourier sine series, you really should know the orthogonality relations for sine and cosine by now, and how they are derived. Heres a first step: $\sin x \cos y = \frac{1}{2} \left( \sin(x-y) + \sin (x+y) \right)$.

 

[tiny-tim]

hi dnp33!

use one of the standard trigonometric identities …

2sinAcosB = sin(A+B) + sin(A-B)

 

[dnp33]

Seeing as you are finding a Fourier sine series, you really should know the orthogonality relations for sine and cosine by now, and how they are derived. Heres a first step: $\sin x \cos y = \frac{1}{2} \left( \sin(x-y) + \sin (x+y) \right)$.

I am aware of the orthogonality relations, however I am not familiar with how they are derived, that is not covered in my textbook unfortunately. I do know that sin and cos are orthogonal on the interval -L to L, but they are not orthogonal on the interval 0 to L (according to my text), so this doesn't help me unfortunately.

 

[dnp33]

Worked perfectly! Thanks a lot.

hi dnp33!

use one of the standard trigonometric identities …

2sinAcosB = sin(A+B) + sin(A-B)

 

[Gib Z]

I am aware of the orthogonality relations, however I am not familiar with how they are derived, that is not covered in my textbook unfortunately. I do know that sin and cos are orthogonal on the interval -L to L, but they are not orthogonal on the interval 0 to L (according to my text), so this doesn't help me unfortunately.

Actually, what I said would have helped you if you weren't so busy trying to be offended. It wasn't just knowing the orthogonality relations that helps here, but knowing how they are derived, as the same first ideas apply to this similar problem. The last sentence of my post was the same identity tiny-tim posted, but perhaps you didn't see it.

 

[dnp33]

I'm sorry if I came off as offended and defensive. I wasn't trying to.

I did notice after that you had the same identity written down as tiny tim, but I had already posted twice and didn't want to go back and post again.

I'll respond more carefully in the future so this doesn't happen again.