Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

R method

  1. Dec 6, 2006 #1
    Can someone tell me why Asin(ax)+Bcos(ax) always gives another sinusoidal wave?
  2. jcsd
  3. Dec 6, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Because you can rewrite that expression into a sinusoidal form.
  4. Dec 7, 2006 #3
    and can that answer be translated into a more mathematical reason?
  5. Dec 7, 2006 #4
    Try it out...
    put A = C*cos(d) B = C*sin(d) where C and d are arbitrary constants. Of course you can put sin in the place of cos and vice-versa, and still get a sinusoidal wave.
  6. Dec 7, 2006 #5
    [tex]A\sin ax + B \cos ax = R \sin (ax+b)[/tex]

    Expanding the right hand side gives you [tex]R\sin ax \cos b + R \cos ax \sin b[/tex]

    This gives [tex]R \cos b = A[/tex] and [tex]R \sin b = B[/tex], therefore [tex]b = \tan^{-1}\frac{B}{A}[/tex].

    A similar method gives you R in terms of A and B, thus turning your sum of trig functions into another, single, trig function. :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: R method
  1. Solve in R (Replies: 17)

  2. Find a and r (Replies: 5)

  3. R^2 or R^3? (Replies: 3)

  4. Exhaustion methods (Replies: 3)