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B Rotating line - x axis point

  1. Jul 14, 2016 #1

    (I hope this is the right place to post this - sorry if it's not)

    Say I have a line (in the graphic is shown a 10mm but it could be any length) and it rotates around a point at one end.

    What is the formula to get the length along the x axis directly under the other end of the line. In the graphic that would be the distance between points a and x.



    The image is not showing so here is the link the my Hotmail onedrive file


    EDIT - I have tried using a Taylor Series but it's been a long time since I was a school :-)
    It's simple on a calculator with the cosine of the angle and the line as a hypotenous but I am trying to get the maths formula.
    Last edited: Jul 14, 2016
  2. jcsd
  3. Jul 14, 2016 #2


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    Staff: Mentor

    It is ##x = 10 \, mm \cdot \cos (\angle{a})##.
    In a right triangle ##\cos (a) = \frac{adjacent}{hypotenuse} \; , \; sin (a) = \frac{opposite}{hypotenuse}## and ##tan (a) = \frac{opposite}{adjacent}.##
  4. Jul 19, 2016 #3
    for angle ##a## made by line with x axis,length along x axis will be ##10\ cos(a)##
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