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Power-amplification formula

  1. Feb 17, 2014 #1
    1. The problem statement, all variables and given/known data

    If exist a formula for reducion of power for sin and cos:

    81f00e549acd8c0fa3f17849ed95f04b.png

    a08ebbfea6efb2d1a12277214402cffb.png

    So, is possible to define a formula of "amplification of power" for sin and cos?

    [tex]\sqrt{\sin(x)} = ?[/tex][tex]\sqrt{\cos(x)} = ?[/tex]

    2. Relevant equations

    imagem.jpg

    3. The attempt at a solution

    None attempt well succeful or relevant.
     
  2. jcsd
  3. Feb 17, 2014 #2

    Ray Vickson

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    Since ##\sqrt{\sin(x)}## and ##\sqrt{\cos(x)}## do not exist (as real quantities) whenever the sin or cos are < 0, any kind of formula would need to be genuinely weird. If there were formulas at all they would need to have branch cuts in the complex plane.
     
  4. Feb 18, 2014 #3
    I didn't understand your answer.
     
  5. Feb 19, 2014 #4

    haruspex

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    Ray is saying, suppose f(x) = √(sin(x)), where f(x) is a real function. How will it give the right answer when sin(x) is negative?
     
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