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Math Help - Solve each equation for 0 < theta < 2(pie)

  1. #1
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    Solve each equation for 0 < theta < 2(pie)

    Solve each equation for 0 < theta < 2(pie)

    tan^2(theta) + 2tan(theta) - 5 = 0

    I can't even remember how to do this...a little help? Please and thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jeavus View Post
    Solve each equation for 0 < theta < 2(pie)

    tan^2(theta) + 2tan(theta) - 5 = 0

    I can't even remember how to do this...a little help? Please and thanks!
    it is quadratic in \tan \theta so treat it as you would a quadratic equation
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  3. #3
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    I'm sorry Jhevon, but I just don't know how to approach it.

    I've tried using the identity tan(theta) = sin(theta)/cos(theta), but I can't set it up.
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  4. #4
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    I could substitue tan(theta) for x to make it:

    x^2 + 2x - 5 = 0

    Would I have to use to solve for the roots?
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    Quote Originally Posted by Jeavus View Post
    I could substitue tan(theta) for x to make it:

    x^2 + 2x - 5 = 0

    Would I have to use to solve for the roots?
    yes, that's what i meant it was quadratic in tan. you have to remember to replace x with tan(theta) when done though to find theta
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  6. #6
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    When subbing in for 4ac though...you get a negative number in the square root.

    What then?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jeavus View Post
    When subbing in for 4ac though...you get a negative number in the square root.

    What then?
    no, the number is positive. you have a negative times a negative times a positive, the result is positive
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  8. #8
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    Hmm...I'm still not getting the answers it is giving:

    0.97, 1.85, 4.11, 5.00 (in the textbook)

    After doing calculations, the 2 roots are:

    x = 0.449
    x2 = 4.449

    I convert both xs back into tan(theta).

    tan(theta1) = 0.449
    tan(theta2) = 4.449

    Solve for both degree.

    tan(theta1) = 24.2 degrees
    tan(theta2) = 77.3 degrees

    Convert both to radians.

    theta1 = 0.422
    theta 2 = 1.34

    Which do not resemble the answers in the textbook. I'm lost.
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Jeavus View Post
    Hmm...I'm still not getting the answers it is giving:

    0.97, 1.85, 4.11, 5.00 (in the textbook)

    After doing calculations, the 2 roots are:

    x = 0.449
    x2 = 4.449

    I convert both xs back into tan(theta).

    tan(theta1) = 0.449
    tan(theta2) = 4.449

    Solve for both degree.

    tan(theta1) = 24.2 degrees
    tan(theta2) = 77.3 degrees

    Convert both to radians.

    theta1 = 0.422
    theta 2 = 1.34

    Which do not resemble the answers in the textbook. I'm lost.
    you solved for the x's wrong somehow
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  10. #10
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    x = (-b)+/- ((sqroot)(2^2 - 4(1)(-5)))/2)1)

    Is that not correct?
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  11. #11
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    Quote Originally Posted by Jeavus View Post
    x = (-b)+/- ((sqroot)(2^2 - 4(1)(-5)))/2)1)

    Is that not correct?
    we have x = \tan \theta = \frac {-2 \pm \sqrt{2^2 - 4(1)(-5)}}2

    now simplify and solve for \theta (remember to use referefernce angles to get all the angles in 0 \le \theta \le 2 \pi. as the answer tells you, you should have 4 angles not just two
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