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Math Help - Re-arranging equation

  1. #1
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    Re-arranging equation

    Hi,

    Any help re-arranging the equation below would be greatly appreciated

    The following equation needs re-arranging to work out alpha (a)

    Phase max = 90 - (2 * tan-1 (sqrt a))

    In the actual problem my phase max = 14.14 and I know that the value of alpha (a) should work out to be 0.6072
    I need to be able to derive the equation above in an upcoming exam so any help would be appreciated

    Thanks

    Dave
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Re-arranging equation

    Quote Originally Posted by db52174 View Post
    Hi,

    Any help re-arranging the equation below would be greatly appreciated

    The following equation needs re-arranging to work out alpha (a)

    Phase max = 90 - (2 * tan-1 (sqrt a))

    In the actual problem my phase max = 14.14 and I know that the value of alpha (a) should work out to be 0.6072
    I need to be able to derive the equation above in an upcoming exam so any help would be appreciated

    Thanks

    Dave
    I'm going to call "Phase max" P for convenience.

    First isolate the inverse tangent:
    P = 90 - (2~tan^{-1} (\sqrt a))

    tan^{-1} (\sqrt a) = \frac{90 - P}{2}

    tan \left ( tan^{-1} (\sqrt a) \right ) = tan \left ( \frac{90 - P}{2} \right )

    Can you take it from here?

    -Dan
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