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    Psychiccleo21's Avatar
    Psychiccleo21 Posts: 2, Reputation: 1
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    #1

    Dec 8, 2007, 04:38 PM
    Inverse functions/ unit circle
    How do I solve this?

    Question: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 pi)

    3tan^2x - 11sec x + 13 = 0
    s_cianci's Avatar
    s_cianci Posts: 5,472, Reputation: 760
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    #2

    Dec 8, 2007, 04:44 PM
    Start by changing everything to sin and cos. Then combine everything into 1 single rational expression. It falls into place from there.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #3

    Dec 8, 2007, 05:29 PM
    Another way is to remember that

    Then we have:





    Now, let

    We get:

    Now, solve the quadratic.
    Psychiccleo21's Avatar
    Psychiccleo21 Posts: 2, Reputation: 1
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    #4

    Dec 8, 2007, 07:37 PM
    Quote Originally Posted by Psychiccleo21
    How do i solve this?

    Question: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2 pi)

    3tan^2x - 11sec x + 13 = 0
    I had it figured up to the point where I had cos x = 3/5 and cos x = 1/2, but after that, I had no idea what to do. I know I can find the points where cos = 1/2 by looking on a unit circle, but 3/5..

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