1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A trigonometric problem

  1. Sep 16, 2006 #1
    Hi. I have to show that
    x(t)=c1 cos(wt) + c2 sin(wt) '(1)'
    and
    x(t) = A sin(wt + phi)
    are equivalent. I know I have to use
    sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)
    or
    cos(alpha +beta)= cos(alpha)cos(beta) - sin(alpha)sin(beta)

    I have been strugling with this problem for a long time, trying to multiply expression (1) with cos(beta) and so on but I don't think I am getting anywere. Could someone please give me a little hint how to begin on this problem?
     
  2. jcsd
  3. Sep 16, 2006 #2

    Astronuc

    User Avatar
    Staff Emeritus
    Science Advisor

    Try applying sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) to x(t) = A sin(wt + phi)

    Let alpha = wt and beta = phi, and since phi is some constant (phase angle), then sin(phi) and cos(phi) are constants.
     
  4. Sep 17, 2006 #3
    That was easy.
    Thanks.:smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...