1. Not finding help here? Sign up for a free 30min 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!

Wave formula

  1. Sep 5, 2005 #1
    why can y(t) = A cos[omega(t)]+bsin[omega(t)]
    equal Ccos[omega(t)-sigma], where C=(A^2 + B^2)^(1/2) and
    tan(sigma)=B/A?
     
  2. jcsd
  3. Sep 6, 2005 #2

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Well

    [tex]\cos(a-b) = \cos a \cos b + \sin a \sin b[/tex]

    Try expanding out [itex]C\cos(\omega t - \sigma)[/itex] using that formula, and see what you get.
     
  4. Sep 6, 2005 #3
    i got C[cos(wt)cos(sigma)+sin(wt)sin(sigma)]...
    am i missing a step?
    @@a
     
  5. Sep 7, 2005 #4

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Now define A=Ccos(sigma) and B=Csin(sigma).

    What do you get if you eliminate sigma from these two equations?
     
  6. Sep 8, 2005 #5
    C[cos(wt)A/C + sin(wt)B/C]= the orignal equation!
    thanks!
     
  7. Sep 10, 2005 #6

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Note also that [itex]A^2 + B^2 = C^2[/itex] and tan(sigma) = B/A, with the given definitions.
     
  8. Sep 12, 2005 #7
    cool! thanks again! :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Wave formula
  1. Interest Formula (Replies: 2)

Loading...