1. Limited time only! Sign up for a free 30min personal 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!

Trig Identity problem

  1. Oct 8, 2014 #1
    I can't quite work out this derivation I ran into which is essentially...Asin^2(wt) + Bcos^2(wt) = A = B. Is this correct?

    I know that sin^2(wt) + cos^2(wt) = 1, but I can't reason out how the factoring works here? Any help?
  2. jcsd
  3. Oct 8, 2014 #2

    Char. Limit

    User Avatar
    Gold Member

    Where exactly did you run into it? Can you paste some context for us to look at?

    Looking at what you wrote, as long as A = B, the full statement is true... but if that's the case, then you might as well just use A.
  4. Oct 8, 2014 #3
    Actually, you can can find the full equation here at the bottom of the screen at 1:20 -

    So A and B are not the same. In effect, its Asin^2(wt) + Bcos(wt) = constant, where the constant is Energy in this case, but the guy doesn't do the deriviation, he just presents the equation and I'm not clear on how he factored it.
  5. Oct 8, 2014 #4


    User Avatar
    Science Advisor

    I think you are misunderstanding what he is saying. It is not that "A sin^2(x)+ B cos^2(x)" is a constant- it is only for these specific, and related, A and B. And he is not using any trig identity. He is simply stating that the "A sin^2(x)+ B cos^2(x)" is the total energy and, because of "conservation of energy", must be constant. Of course, taking x= 0 gives "B" and taking x= pi/2 gives "A" so A and B must be equal to that constant and so to each other.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook