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Math Help - arc functions

  1. #1
    Newbie
    Joined
    Nov 2008
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    5

    arc functions

    Find the exact value (no decimals) for:
    sec(arctan 3)
    arcsin(sin2pi/3)
    arcsin((root3)/2)


    Lastly, write an algebraic expression for:
    cos(arcsin 1/(x-1))

    Thanks guys. Finals soon and I am working on some practice.
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  2. #2
    Newbie darthfader's Avatar
    Joined
    Apr 2009
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    Philippines
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    10
    Hi trigcalc4! Let me try the first one for you.

    sec (arctan 3)

    Let arctan 3 = x
    Then  tan x = 3

    We know that tan\theta in a right triangle is OPPOSITE/ADJACENT, so we can assume that Opposite = 3 and Adjacent is = 1 so the hypotenuse is \sqrt{10} by Pythagorean Theorem.

    We also know that \sec x is equal to HYPOTENUSE/ADJACENT so

    sec x = \frac{\sqrt{10}}{1} = \sqrt{10}

    We know that x =\arctan{3}
    So we're done!

    The others are relatively easier and you can try them by yourself.
    If your still confused feel free to ask again.

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