How Do You Calculate (X,Y) Coordinates on a Circle with a Given Radius?

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SUMMARY

The discussion focuses on calculating (X,Y) coordinates on a circle with a radius of 10 inches, centered at (0,10). The key formula derived is x² + y² = 10², which can be adapted for circles not centered at the origin using (x - a)² + (y - b)² = r², where (a,b) is the center and r is the radius. The user also seeks software recommendations for quickly solving for various points on the circle.

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  • Understanding of trigonometric functions: sine and cosine
  • Familiarity with the Cartesian coordinate system
  • Basic knowledge of algebraic equations
  • Concept of radius and circle geometry
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  • Learn about parametric equations for circles
  • Explore software tools for geometric calculations, such as GeoGebra
  • Investigate the application of polar coordinates in circle calculations
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I would like to calculate (X,Y) coords on a circle with a 10" radius.

I have some idea on how this can work but I'm not real solid on it. Say the center is (0,10) and I'd like to solve for Y given an arbitrary X. How would I do this? Obviously (10,0) and (-10,0) and (0,-10) and I know that sin and cos are going to come into it but not sure the actual formula here.

Any help would be greatly appreciated.

EDIT: Thinking a little bit sin()=opp/hyp and cos()=adj/hyp. opposite would be my Y travel and adjacent would be my X. And the radius=10. Theta would be 2*pi/?.
 
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It's [itex]x^2 + y^2 = 10^2[/itex]. You can do [itex](x - a)^2 + (y - b)^2 = r^2[/itex] for an arbitrary center point (if the circle is not centered at the origin). In such a case the point (a, b) is your center and 'r' is your radius value.
 
Ok, thanks. So I WAY over complicated things. Thanks for the help there.

As far as quick easy solving for various points, do you (or anyone else for that matter) have any software recommendations?
 
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