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Math Help - PreCal questions..

  1. #1
    Newbie
    Joined
    Dec 2008
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    PreCal questions..

    can someone explain how to do this kind of problem using the unit circle and all in explicit detail please?

    1: sin(arctan -1)
    2: cos(arc csc 13/5)

    just problems like that because i have no idea how to solve them.

    Thanks.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    You can start with tan(Arctan \theta) = \theta

    \frac{sin(Arctan \theta)}{cos(Arctan \theta)} = \theta

    \frac{sin^2(Arctan \theta)}{cos^2(Arctan \theta)} = \theta^2

    \frac{sin^2(Arctan \theta)}{1 - sin^2(Arctan \theta)} = \theta^2

    \frac{1 - sin^2(Arctan \theta)}{sin^2(Arctan \theta)} = \frac{1}{\theta^2}

    \frac{1}{sin^2(Arctan \theta)} -1 = \frac{1}{\theta^2}

    \frac{1}{sin^2(Arctan \theta)} = 1 + \frac{1}{\theta^2} = \frac{1 + \theta^2}{\theta^2}

    {sin^2(Arctan \theta)} = \frac{\theta^2}{1 + \theta^2}

    {sin^2(Arctan (-1))} = \frac{1}{2}

    Arctan(-1) is an angle between -\frac{\pi}{2} and 0
    Therefore sin(Arctan(-1)) is negative

    {sin(Arctan (-1))} = -\frac{\sqrt{2}}{2}
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