Suppose that the coordinates of $\displaystyle A: (x,y)$.
Suppose that $\displaystyle x\cdot y\ne 0 $ then
$\displaystyle \Theta=Arg(x,y) = \left\{ {\begin{array}{{lr}} {\arctan \left( {\frac{y}{x}} \right),}&{x > 0} \\ {\arctan \left( {\frac{y}{x}} \right) + \pi ,}&{x < 0\;\& \;y > 0} \\ {\arctan \left( {\frac{y}{x}} \right) - \pi ,}&{x < 0\;\& \;y < 0} \end{array}} \right. $
Then $\displaystyle \Theta$ is the measure of the angle the vector $\displaystyle \vec{C}$ makes with the positive $\displaystyle x\text{-axis}~.$
Now the coordinates of $\displaystyle B: (r\cos(\Theta),r\sin(\Theta))$ where $\displaystyle r$ is the radius of the circle.