# Solving Fourier Coefficients: Hints for Finding a_n

• errordude
In summary, the conversation is about finding the Fourier series for a given function and the person is struggling to get the correct answer due to a mistake in calculating b1. They receive hints and suggestions from others and eventually realize their mistake.
errordude

## Homework Statement

Hi i would just like some fast hints, I'm doing the integrals wrong, I am splitting up the integral below and get the wrong answer.

well it's about finding the Fourier series for f(t)={0 for -π<t<0 and sint for 0≤t≤π}

## Homework Equations

$$a_{n} = \frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\cos(nt) dt , n\in Z_{+}$$

## The Attempt at a Solution

well i split the integral up in finding $$a_{n}$$ like

$$\frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\cos(nt) dt = \frac{1}{\pi}\int_{-\pi}^{0} 0· dt+\frac{1}{\pi}\int_{0}^{\pi}\sin(t)\cos(nt) dt$$
Both of these elementary, but it fails to produce the right series.
Hints anyone?

Did you forget the bn?

LCKurtz said:
Did you forget the bn?

no but that just get to zero

errordude said:
no but that just get to zero

They can't be zero because the function you are expanding is not an even function.

LCKurtz said:
They can't be zero because the function you are expanding is not an odd function.

That's what i was thinking

$$\frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\sin(nt) dt = \frac{1}{\pi}\int_{-\pi}^{0} 0· dt+\frac{1}{\pi}\int_{0}^{\pi}\sin(t)\sin(nt) dt$$

but the above is zero!

i'm doing something wrong.

I have to run now. You didn't show your work but I'm guessing you need to look what happens when n = 1.

halloo??

any1 who knows this Fourier series

f(t)={0 for -π<t<0 and sint for 0≤t≤π}

Nobody is going to just give you the answer. Show us your work for the an and bn and we will help you find the mistake.

LCKurtz said:
Nobody is going to just give you the answer. Show us your work for the an and bn and we will help you find the mistake.

Hey man chill.

b_1=1/2 that was the problem.

errordude said:
Hey man chill.

b_1=1/2 that was the problem.

Chill?? Surely you mean "Thanks for the suggestion, eh?"

LCKurtz said:
Chill?? Surely you mean "Thanks for the suggestion, eh?"

you were right LC, b_1 was the crucial step.

thanx

## What is the purpose of finding Fourier coefficients?

The purpose of finding Fourier coefficients is to represent a periodic function as a sum of sinusoidal functions. This allows us to analyze and manipulate the function in a simpler form.

## How do you find the Fourier coefficients of a function?

To find the Fourier coefficients of a function, we use the Fourier series formula which involves integrating the function over one period with respect to the trigonometric functions (sine and cosine).

## What are some hints for finding the Fourier coefficients?

Some hints for finding the Fourier coefficients include using trigonometric identities, splitting the function into even and odd parts, and using symmetry of the function to simplify the integration process.

## What is the significance of the coefficient an in the Fourier series?

The coefficient an represents the amplitude of the cosine term in the Fourier series. It tells us how much of the cosine function is needed to reproduce the original function.

## What happens if we increase the number of terms in the Fourier series?

If we increase the number of terms in the Fourier series, the approximation of the function will become more accurate. This is because we are adding more sinusoidal functions to better represent the original function.

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