Integrating a Product of CosinesDate: 05/04/2005 at 04:21:24 From: Peter Subject: An integral involving cosine Let n and m be natural numbers. My book says that the integral from -pi to pi of the function f(x) = cos(nx) * cos(mx) is 1) pi if n = m 2) 0 else. I can't figure out how to prove this. Date: 05/04/2005 at 09:09:13 From: Doctor Jerry Subject: Re: An integral involving cosine Hello Peter, What you need is the "product to sum formula" from trigonometry: cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) cos(a-b) = cos(a)*cos(b) + sin(a)*sin(b) Adding, cos(a)*cos(b) = (1/2)(cos(a+b) + cos(a-b)) Use this to change the integrand to a sum. Please write back if my comments are not clear or if you need more help with this problem. - Doctor Jerry, The Math Forum http://mathforum.org/dr.math/ Date: 05/04/2005 at 09:29:34 From: Peter Subject: Thank you (An integral involving cosine) Hi, Doctor Jerry. Thank you for the perfect answer. Everything is now clear. Peter |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/