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Derivation of formula for general formula of sine equations

  1. Jun 25, 2012 #1
    My book gives the following formulas for the general solution of sine equations (if sin(x)=a)

    [tex]x=2n\pi + sin^-^1(a)[/tex]


    [tex]x=(2n+1)\pi - sin^-^1(a)[/tex]

    [tex]x=n\pi + (-1)^nsin^-^1(a)[/tex]

    But it doesn't explain how it got them. I can easily see how they got the first two but I have no idea how they got the more general one. My teacher didn't show how it was derived either...just threw a bunch of formulas at us to remember
  2. jcsd
  3. Jun 25, 2012 #2


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    Take the equation

    [tex]x=n\pi + (-1)^n \sin^{-1}(a)[/tex]

    What happens if you take n even (that is: of the form 2k) and what happens if you take n odd (that is: of the form 2k+1)??
  4. Jun 25, 2012 #3
    ^ Wow, it seems so obvious now but I never would've seen had you not pointed me in the right direction, thank you!
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