Fourier Series (differentiation)

[driedupfish]

Homework Statement

sin(t)cos(nt) dt

Homework Equations

The Attempt at a Solution

I tried setting u=sin(t) or cos(nt) or nt but none seems to work. Can someone give me a hint as what to set u equal to? Thanks.

 

[Pengwuino]

Are you trying to integrate? Over what range?

 

[driedupfish]

Are you trying to integrate? Over what range?

The function is as follow:
f(t)= 0, -pi ≤ t ≤ 0
sint, 0 ≤ t ≤ pi

≤ (less than or equal to)

I just don't know what to set u equal to, I am thinking of using integration by substitution.

 

[driedupfish]

Can someone give me some hints please?

 

[lanedance]

I would start by trying the first few cases by hand n=0, n=1, n=2, n=3, etc.. and see if a pattern develops, both on result and how to evaluate

look at some trig formulas for angle sums & double angle may help before looking at substitution