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Math

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I am stuck on a problem that has to do with the double angle formulas. I have to solve this: 4sinxcosx = 1. I tried using the formula 2sinu = 2sinucosu by substituting it in like this: 2(2sinxcosx)= 1 but then I am stuck

  • Math -

    remember that sin 2x = 2sinxcosx

    so 4sinxcosx = 1
    2(2sinxcosx) = 1
    2(sin2x) = 1
    sin2x = 1/2

    I will assume you are working in degrees, we can always switch later on

    so 2x = 30° or 2x = 150° because of the CAST rule
    x = 15° or x = 75°

    the period of sin 2x is 180°, so adding 180 to any answer will produce new answers

    x = 15°, 195°, ...
    or
    x = 75°, 255°, ...

    In Radians:
    15° = π/12 radians
    x = π/12, 13π/12....
    x = 5π/12, 17π/12, ...

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