A trigonometric problem

  • Thread starter Knight
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  • #1
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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?
 

Answers and Replies

  • #2
Astronuc
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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.
 
  • #3
6
0
That was easy.
Thanks.:smile:
 

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