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Find angle from involute

  1. Feb 4, 2005 #1
    This is my first post and I am not sure how to get the math symbols used in formulas.
    The formula for the involute of an angle is: involute of theta = tangent of theta - pi * theta / 180.
    If I know the involute of theta how do I solve for theta?
  2. jcsd
  3. Feb 4, 2005 #2


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    Is that tan(theta- pi*theta/180) or tan(theta)- pi*theta/180?? Parentheses are important!

    Guessing that it is the former, use the arctan!
  4. Feb 4, 2005 #3
    No it is the latter tan(theta)- pi*theta/180

    example .014904=tan(20)-pi*20/180
  5. Feb 4, 2005 #4


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    Hmm, now that's much harder. In general you cannot get a "formula" solution to a transcendental equation, which this is, with the unknown both inside and outside a transcendental function (tangent). A numerical solution is probably the best you can do.
  6. Feb 4, 2005 #5
    A numerical answer is what I am looking for in the end. This is the situation. I have an Excel spreadsheet with some formulas for figuring the measurement over wires of special thread forms. One formula gives me the involute of an angle. I then have to look up the coresponding angle in a table and enter that angle in the next formula. I am trying to come up with a way to calculate the angle without having to look in the table. If the angle is accurate to three decimal places this should be fine for my needs. I would greatly appreciate any help
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