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!

Transform General EQ Acos(wt)+Bsin(wt)

  1. Jan 19, 2016 #1

    RJLiberator

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Show that Ccos(wt+phi) = Acos(wt)+Bsin(wt)
    2. Relevant equations
    Trig identity that states cos(wt+phi) = cos(wt)cos(phi)-sin(wt)sin(phi)

    3. The attempt at a solution

    Ccos(wt+phi)=(Ccos(phi))cos(wt)+(-Csin(phi))sin(wt)
    let A = Ccos(phi)
    Let B = -Csin(phi)

    Ccos(wt+phi) = Acos(wt)+Bsin(wt)
    and done.

    Is this as simple as I have shown? Or am I making a critical mistake in letting A = Ccos(phi) and B = -Csin(phi)?
    Is there a more rigorous way of doing this that would be expected?

    Since phi is a constant, C is a constant, I would think that this is a suitable way to prove that these two sides are equal, but I can't help but feel a bit weak here about this.
     
  2. jcsd
  3. Jan 19, 2016 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes, it is just that simple.
     
  4. Jan 19, 2016 #3

    RJLiberator

    User Avatar
    Gold Member

    Excelent. Thank you for the confirmation, then I know I am on the right track.

    Now the question states to express C and phi as a function of A and B. In this case, I set the equations equal to each other
    Ccos(wt+phi) = Acos(wt)+Bsin(wt) and isolate C and phi, I assume.
     
  5. Jan 19, 2016 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Going in this direction can be a bit trickier. The results you have in the OP should help with this.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Transform General EQ Acos(wt)+Bsin(wt)
Loading...