You are Here: Home >< Maths

# fourier series - sketching graphs

Announcements Posted on
TSR's new app is coming! Sign up here to try it first >> 17-10-2016
1. Show that the half range Fourier cosine series of the function f(x) = x^2 on the interval [0,1] is given by:

Sketch f(x) and the functionto which its half-range Fourier cosine series converges on the interval [-3,3].

I can do the first past of the question fine, but I'm really poor at drawing these graph and always seem to get them wrong. Can someone please give me a general guide of what they would do to draw graphs for questions similar to this? I don't understand how to plot any points at all..

2. Write C(x) for your cosine series.
You know C(x) = x^2 on [0,1]
Since C(x) is a cosine series, you know C(-x)=C(x).
So now you know what C(x) is on [-1,1].
Finally, C(x) has period 2, so C(x+2)=C(x). This is enough to let you draw C(x) for the entire interval [-3,3].
3. Thanks for that DFranklin, think I've got the hang of it now...would you mind checking the attached file though just to make sure it's right? I've tried doing the graph to the question below as well. I think I'll have Fourier Series in the bag if these are right

for and for

Sketch f(x) and the function to which its Fourier series converges on the interval -3pi to 3pi.
Attached Images

4. Looks OK, but no guarantees. I suggest running the equations through a graphing program if you want to be sure. (You could also use Excel or similar).

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: April 19, 2008
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### How does exam reform affect you?

From GCSE to A level, it's all changing

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams