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Basic Trig I've forgotten

  1. May 16, 2008 #1
    So I think this falls under the stuff I've forgotten file. We're writting a program for the CNC lathe and I need to find x and y coordinates of a partial arc radius given the angle. This trick is the controller doesn't have sine and cosine funcitonality. I'm sure this is a basic definition thing I learned in trig in High School, unfotunately the 15 years since then have killed that memory. Help?

  2. jcsd
  3. May 16, 2008 #2


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    You probably just need x^2 + y^2 = r^2
  4. May 16, 2008 #3
    I looked at that but I'm gonna need more. Basically we want the user to input the angle. The Pythagorean theorum gets me one equation and two unknowns, I need to come up with another equation or be able to use something to generate the sine ratio without using the sine funciton.
  5. May 16, 2008 #4


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    Sine is pretty easy to approximate.

    If the angle is less that 30 degrees then the approximation,

    sin(x) = x, with x in radians ( equiv to sin(x) = x*pi/180 with x in degrees),

    will get you less than 5% error.

    If you want better use sin(x) = x - x^3 / 6 (equiv to six(x) = x*pi/180 - (x*pi/180)^3 / 6 with x in degrees) will get you approx 1% max error if x is less than 60 degrees and better than 0.1% max error if x is less than 30 degrees.
    Last edited: May 16, 2008
  6. May 16, 2008 #5


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    Yep wat uart said was 100% correct, and for the cosine function you may want to use [tex]cos(x)[/tex] = [tex]\pi[/tex] - [tex](x*\pi/180)^{2}/2[/tex] with similar accuracy. for more accuracy just add ...[tex]+ (x*\pi/180)^{4}/24[/tex]
  7. May 16, 2008 #6
    When evaluating the polar form of complex numbers I hate dealing with angles in the 2nd, 3rd and 4th quadrants.
  8. May 19, 2008 #7
    Thanks for the help! I actually just stumbled on a site showing how to use a Tayor series to estimate sine and cosine ([w__.homeschoolmath.net/teaching/sine_calculator.php) and how calculators etc. use a CORDIC algorithm to caclutate the value. Guess it wasn't actually a simple thing I forgot. Of course then I went back to one of my old math books and there it was. Thanks again!

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