angle in a circle

Posted on 2007-10-13
Medium Priority
Last Modified: 2013-12-26
 markww    Member since: 4/5/2007
 Posted - 10/13/2007 2:19:29 PM

I have a circle, I know its radius. I have a point on its edge. Is there anyway to figure out what angle in degrees that is?

      /         |        \    
     P         |         \  
     |          |           |
     |          |           |
      \         |         /
       \------|---- /

yeah that's a fine ascii circle, so anyway, I'm interested in the angle formed between P, O, X. I know the coordinates of all 3, I just want to know the angle between them.

Thanks for any help

p.s. - the formatting keeps messing up the circle (not that it was that great to begin with, hope it's understandable)
Question by:DJ_AM_Juicebox
  • 3
LVL 22

Accepted Solution

NovaDenizen earned 2000 total points
ID: 20071925
atan2(py,px) returns the angle from x counterclockwise in radians.  To convert to degrees, multiply the answer by 180/pi.  If you need the answer to always be positive (range 0 to 360 instead of -180 to 180) then add 360 when the value is negative.
LVL 85

Expert Comment

ID: 20072456
in  general arccos( (X-O) dot (P-O) / (|X-O| * |P-O|) )

Expert Comment

ID: 20072713
Use your cordinates to determine the length of the intercepted arc between p and x. The angle in radians = the length of the arc / the length of the radius.  The formula found in my Trig book is omega = s / r.  Then convert radians to degrees with 2 pi radians = 360 degree (circumference of a circle).

I don't remember and not able to quickly find how to get the length of the arc segement.  Will let you know if I find out.  Please give details of the coordinates and other information you have about this problem.
LVL 85

Expert Comment

ID: 20072950
You can find the arc from the cosine of the dot product
LVL 85

Expert Comment

ID: 20072955
If you already know |a| = |b| = radius then you only need a · b

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