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math

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solve the following trig equation :
7 = 8sin(1/2)x. I can solve this using the half-angle indentity. But i need to solve this using period and phase change equation. how do i do this?

  • math -

    7 = 8sin(1/2)x

    sin (1/2)x = .875

    so (1/2)x is in the first or second quadrant, and
    (1/2)x = 61.04º or (1/2)x = 118.96º

    then x = 237.9º or 122.1º

    but the period of your curve is 720º

    so by adding/subtractin 720º to/from any of the found angles will give you more answers.

    in general
    x = 122.1 + 720k or
    x = 237.9 + 720k , where k is an integer.

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