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Math Help - Exact Values and Trigonometric Equations

  1. #1
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    Smile Exact Values and Trigonometric Equations

    Determine all the possible values of x where 0 degree <= x <= 360 degree such that

    sec^2 x + sec x = 2
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  2. #2
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    Re: Exact Values and Trigonometric Equations

    Hey choi105.

    Can you show us what you have tried?
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  3. #3
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    Re: Exact Values and Trigonometric Equations

    sec^2 x + sec x = 2
    (sec x - 1)( sec x + 2) = 0
    sec x - 1 = 0 or sec x + 2 = 0
    sec x = 1 or sec x = -2
    1/cos x = 1 or 1/cos x = -2

    then i don't know how to continue...
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  4. #4
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    Re: Exact Values and Trigonometric Equations

    There are exact values for +-1/2 and +-1. (Hint Consider pi/2, pi/3 and 2pi/3)
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  5. #5
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    Re: Exact Values and Trigonometric Equations

    Quote Originally Posted by choi105 View Post
    sec^2 x + sec x = 2
    (sec x - 1)( sec x + 2) = 0
    sec x - 1 = 0 or sec x + 2 = 0
    sec x = 1 or sec x = -2
    1/cos x = 1 or 1/cos x = -2

    then i don't know how to continue...
    Surely you can see where \displaystyle \cos{(x)} = 1 and \displaystyle \cos{(x)} = -\frac{1}{2}...
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