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Math Help - How to find theta in a given trig function (pre-calc)

  1. #1
    Junior Member
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    Mar 2009
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    How to find theta in a given trig function (pre-calc)

    hi guys, I need a little help with trig

    the given:

    if cos theta = -.25 and tan theta > 0

    find the other five trig functions of theta


    what I'm having problems with is how to find what theta is because I have no idea how to find the other trig functions w/o knowing the value of theta (except secant)

    help would be greatly appreciated
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  2. #2
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    Oct 2008
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    \cos(\theta) = \frac{-1}{4} is not a special angle so we construct a right triangle with one point at the origin, one point at (-1,0) and the hypotenuse of the triangle is 4. This is because cos = x-value/hypotenuse.

    We can use pythagorean's theorem to find the other leg of this right triangle.

    4^2 = x^2 + y^2

    with x = -1

    4^2 = (-1)^2 + y^2

    \implies y = \pm \sqrt{15}

    Your told \tan(\theta) > 0, and roughly speaking tan = y-value/x-value. Because the x-value is negative we know the y-value needs to be negative to make the fraction y/x positive.

    So your triangle is in the quadrant III and now you have a triangle from which to get the other trig functions.
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