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Math Help - Trig and geometry problems

  1. #1
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    Trig and geometry problems

    given y = 5x and y = .5x, When the these lines cross, what is the value of tan theta?
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  2. #2
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    Re: Trig and geometry problems

    Assuming \theta is the first-quadrant angle between the two lines, suppose that \alpha is the first-quadrant angle between the x-axis and the line y = 0.5. Then,

    \tan \alpha = 0.5, and
    \tan (\alpha + \theta) = 5.

    Also, \tan (\alpha + \theta) = \frac{\tan \alpha + \tan \theta}{1 - \tan \alpha \tan \theta} = 5.

    Replace \tan \alpha with 0.5, then solve for \tan \theta.
    Last edited by richard1234; June 30th 2012 at 10:01 AM.
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  3. #3
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    Re: Trig and geometry problems

    Quote Originally Posted by Pat722 View Post
    given y = 5x and y = .5x, When the these lines cross, what is the value of tan theta?
    Here is a simple way.
    \theta=\arctan(5)-\arctan(0.5)
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  4. #4
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    Re: Trig and geometry problems

    Darn, should've thought of that. Good solution.
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