My Math Forum Calculating circle's coordinates using radius and rotation?

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 January 25th, 2013, 10:39 AM #1 Newbie   Joined: Jan 2013 Posts: 3 Thanks: 0 Calculating circle's coordinates using radius and rotation? Image here If I know radius of the circle, O's coords and alpha, can I calculate B's coords? I have painted as red that, what, I think, might be helpful. Thank you in advance.
 January 25th, 2013, 10:55 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Calculating circle's coordinates using radius and rotati Let $$$x_O,y_O$$$ be the coordinates of O and $r$ be the radius of the circle, then we may write the coordinates of B as: $$$r\sin(\alpha)+x_O,r\cos(\alpha)+y_O$$$
 January 25th, 2013, 11:41 AM #3 Newbie   Joined: Jan 2013 Posts: 3 Thanks: 0 Re: Calculating circle's coordinates using radius and rotati Many thanks I would also like to ask... is it possible to calculate alpha from B's (and O's) coordinates and $r$?
 January 25th, 2013, 11:46 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Calculating circle's coordinates using radius and rotati Yes, you would have to use the inverse sine and cosine functions along with some attention to which quadrant the relative position of B to O places the angle $\alpha$.
January 26th, 2013, 12:29 AM   #5
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Re: Calculating circle's coordinates using radius and rotati

Quote:
 you would have to use the inverse sine and cosine functions
I was thinking about that all night long, but I'm not good in trigonometry
Can You write whole formula?

 January 26th, 2013, 07:40 AM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Calculating circle's coordinates using radius and rotati It would really be an algorithm rather than a formula. You would have to use conditional statements based on B's relation to O to determine the quadrant of $\alpha$.
 February 19th, 2013, 08:58 PM #7 Banned Camp   Joined: Feb 2013 Posts: 224 Thanks: 6 Re: Calculating circle's coordinates using radius and rotati You know the radius of the circle. That means you can write an equation for that circle. You know the angle of line OB. That means you know the slope, by tangent. If know know the slope of a line and that it intersects the center of the circle, you can write an equation for the line. Solve for x and y as the interception of the circle and the line.

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