Circle in polar coordinates, center and radius

Question

If I have this formula of a circle in polar coordinates $$r=R(cos(\theta)+sin(\theta))$$

Then how can I find the center and radius of it? I've plotted it for $R=4$

Answer 1

Hint

$$\cos x+\sin x=\sqrt{2}\sin\left(x+{\pi \over 4}\right)$$another way is $$r^2=rR(\cos\theta+\sin\theta)\implies x^2+y^2=Rx+Ry$$

Answer 2

Hint: In the figure you drew, the circle crosses the $x$ and $y$ axes three times. Those three crossings determine three points. Three points determine a circle.