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Math Help - Trigonometric Trianle

  1. #1
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    Trigonometric Trianle

    what is the value of X when Q is the biggest?
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  2. #2
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    What is Q?
    (You cetainly do not mean the Q continuum).
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  3. #3
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    Quote Originally Posted by camherokid View Post
    what is the value of X when Q is the biggest?
    Hello,

    I assume that you want to know for which value of x has the angle \theta a maximum.

    From your sketch you see:
    \theta(x)=\arctan\left(\frac{420}{x}\right)-\arctan\left(\frac{380}{x}\right)

    You'll get an extremum if the first derivative of this function equals zero:

    \theta'(x)=\frac{1}{1+\left(\frac{420}{x}  \right)^2}\cdot \left(\frac{-420}{x}\right)-\frac{1}{1+\left(\frac{380}{x}  \right)^2}\cdot \left(\frac{-380}{x}\right)

    After a few and simple transformations you'll get:

    \theta'(x)=\frac{40(159600 - x^2)}{(x^2 + 144400)(x^2 + 176400)}

    That means: \theta'(x)=0\text{ if }159600 - x^2=0. Solve for x. I've got:
    x= 399.4996... \approx399.5

    There is of course a negative solution of x but thisvalue isn't very realistic with your problem.

    EB
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  4. #4
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    Thanks you Earboth...for the solution.
    I knew how to get to the Tan formula...
    but I just did not what to do with it.
    \theta is the angle...but I wrote Q. I don't know
    where I can find that sign.

    Great Job...!
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  5. #5
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    Quote Originally Posted by camherokid View Post
    ...
    \theta is the angle...but I wrote Q. I don't know
    where I can find that sign.
    Hello,

    maybe this will help a little bit further: In this forum you can find a link to the LaTeX-tutorial.

    (If I find the link in time I'll add it here)

    Have a nice time!

    EB

    Edit: Well, Ihope I actually did find the right link: http://www.mathhelpforum.com/math-he...rial-latex.pdf
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