• Support PF! Buy your school textbooks, materials and every day products Here!

Simple cosine expression NOT so simple!

  • Thread starter Mark Wood
  • Start date
  • #1
4
0
:grumpy:

I am rediscovering my long lost "A" level maths and have been having lots of fun working on puzzles. Unfortunately, I seem to have hit something of a wall in the following simple expression that is repelling every attack I launch:

f(x)=[tex]Sqrt[/tex](1+kcos(x))

I have tried substituting x=arccos(w) and w=arccos(w/k), expressing things as logs, mungeing the equations I get, and a number of slightly more desperate attacks, but whatever I do to get rid of one term or provide something that can be cancelled out, a new problem pops up.

I feel that there is a simple answer to this, but the more I look at it the less I can see the way forward.

Any suggestions anyone?
 
Last edited by a moderator:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
What exactly do you want to do with f(x)?
 
  • #3
4
0
Ah! So absorbed by it, I've missed the most important bit!

I'm trying to integrate it to get the area under the curve between x=0 and x=pi
 
  • #4
631
0
Sorry, i couldn't get ur expression. is it (1+kcos(x))^(1/2)
 
  • #5
4
0
Yes it is - the root of (1+kcos(x))
 
  • #6
2,063
2
I don't think it has a solution made up entirely of elementary functions. Elliptic functions may be involved.
 
  • #7
631
0
I too struggled for it for 6-8 months. Its a kind of elliptic integral(which i didn't knew). u might be knowing. u can check it on an integrator at www.wolfram.com
 
  • #8
4
0
Gosh - what a great tip. I didn't know the integrator existed. Thank you.

Having got the answer from Wolfram I'm kind of pleased that I hadn't missed an obvious solution.

Thank you all.
 

Related Threads on Simple cosine expression NOT so simple!

Replies
1
Views
915
Replies
1
Views
7K
  • Last Post
Replies
1
Views
1K
Replies
5
Views
910
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
0
Views
1K
Top