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Math Help - basic trigonometric identities

  1. #1
    Liyo
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    basic trigonometric identities

    I don't know where to begin to do stuff like this-

    if sec theta=3/2, find cos theta.


    or
    use the given information to determine the exact trig value

    cos theta= -2/3, 90 degress<theta<180 degress; sin theta
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Liyo
    I don't know where to begin to do stuff like this-

    if sec theta=3/2, find cos theta.


    or
    use the given information to determine the exact trig value

    cos theta= -2/3, 90 degress<theta<180 degress; sin theta
    The first one isn't so much a trig identity as it is a definition:
    cos\theta=\frac{1}{sec\theta}=\frac{1}{3/2}=2/3

    For the second one, we use probably the most standard trig identity:
    sin^2\theta + cos^2\theta = 1
    So if we have the cosine...
    sin^2\theta+(-2/3)^2=1
    sin^2\theta+4/9=1
    sin^2\theta=5/9
    sin\theta=\pm \sqrt{5/9}

    Now, we are looking for an angle between 90 and 180 degrees. The sine function is positive in this interval. So sin\theta=\sqrt{5/9}. Specifically, we will be finding a value for theta between 0 and 90 degrees, so we are considering the angle we will find to be a reference angle.

    I don't know of any "nice" angle such that the sine of theta will be this value. So find theta using a calculator. Now, this is the reference angle measured from 180 degrees, so we subtract this angle from 180. I get about 131.8 degrees.

    -Dan
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  3. #3
    Member
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    if you're having trouble with it, just draw a picture and break the problem into smaller parts. you know that cos is between 90 and 180 degrees. and that cos \theta =-2/3. so draw a picture. find the length of the other leg using the pythagorean theorem and find sin.
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    Last edited by c_323_h; March 10th 2006 at 05:00 AM.
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