# Polar coords - Range of theta

1. Jun 4, 2012

### Jonmundsson

1. The problem statement, all variables and given/known data
We have the circle $(x - 1)^2 + (y-2)^2 = 1$. Find the boundaries of θ and r.

2. Relevant equations
x = h + rcosθ
y = k + rsinθ

3. The attempt at a solution
This is a circle with its origin at (1,2) and a radius of 1 so r is between 0 and 1 and the circle lies in the first quadrant but touches the x and y axis so theta is between 0 and pi/2

Is this correct? Just curious

edit: additional question: let's say I define y = 2 + rsinθ and x = 1 + rcosθ. Would this circle go from 0 to 2pi? (point of origin (1,2))

2. Jun 4, 2012

### LCKurtz

Your comment in the edit is exactly how to set up the problem. You would put $r = 1$ to get the circle and $0 \le r \le 1$ to get the interior.