How can I obtain real lengths for 'r' in the equation of a circle when R > A?

[tanderse]

Right now, I need to use the equation of a circle to describe a geometry I'm dealing with in a research project. For some reason, I cannot make sense of it, and it is extremely frustrating... Right now I'm using:

r = Rcos(theta)+sqrt(A^2-(Rsin(theta))^2)

where R is the distance from the origin to the center of the circle and A is the radius of the circle. Assume the center of the circle lies on the polar axis. I keep getting complex lengths for 'r', which obviously comes from the negative term in the square root. Can someone explain to me in a physical sense why this is happening? And my main question is how can I make it so I only obtain proper, real lengths for 'r'? Any help is appreciated

 

[Mute]

What do r and theta represent? We can't tell you why your equation is giving you non-nonsensical answers if we don't know what it is, in principle, supposed to mean. Where did your equation come from?

 

[ross_tang]

In short, you are dealing with the case where R > A. In this case, value of $$\theta$$ cannot be arbitrary. If the value of $$\theta$$ is too large, there will be no intersection between the radial line and the circle.

Please refer to this http://www.voofie.com/content/78/why-do-i-get-imaginary-value-for-radius-from-equation-of-circle-in-polar-coordinate/" , which has nice graphs and detailed steps to illustrate the situation.