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A trigonometric problem

  1. Sep 16, 2006 #1
    Hi. I have to show that
    x(t)=c1 cos(wt) + c2 sin(wt) '(1)'
    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)
    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


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    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.
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