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.