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Math Help - Getting negative answer.

  1. #1
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    Exclamation Getting negative answer.

    Given the following equations in the given interval 0 < x < 360

    1 + tan^2x = 3tanx

    i got x = -2.6 and x = -0.4
    since the answers are negative, shudnt i use the 2nd and 4th quadrant to ge to get the answes? The answers at the back of the book use the 1st and 3rd quadrant. Have i gone wrong??????
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  2. #2
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    Quote Originally Posted by Sundae View Post
    Given the following equations in the given interval 0 < x < 360

    1 + tan^2x = 3tanx

    i got x = -2.6 and x = -0.4
    since the answers are negative, shudnt i use the 2nd and 4th quadrant to ge to get the answes? The answers at the back of the book use the 1st and 3rd quadrant. Have i gone wrong??????
    You can use symmetry to solve in any quadrant you wish.

    Quad1: \theta

    Quad2: \pi-\theta

    Quad3: \pi+\theta

    Quad4: 2\pi-\theta
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  3. #3
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    Quote Originally Posted by Sundae View Post
    Given the following equations in the given interval 0 < x < 360

    1 + tan^2x = 3tanx

    i got x = -2.6 and x = -0.4
    since the answers are negative, shudnt i use the 2nd and 4th quadrant to ge to get the answes? The answers at the back of the book use the 1st and 3rd quadrant. Have i gone wrong??????
    correction ...

    <br />
\tan^2{x} - 3\tan{x} + 1 = 0<br />

    \tan{x} = \frac{3 \pm \sqrt{5}}{2}

    \tan{x} = 2.6180

    \tan{x} = .382
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  4. #4
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    x = .382
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  5. #5
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    Quote Originally Posted by pickslides View Post
    x = .382
    correction #2 ... \tan{x} = .382
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  6. #6
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    thx alot, i know what i did wrong i missed off the - in the quadratic formula
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