Shift in origin for polar coordinates

Question

Consider a set of polar coordinates, $(r, \theta)$ for a plane. Let's say there is a point, at $\left(1,\frac{\pi}{4}\right)$ for which I want to define a translated and rotated coordinate system, $(R, \Theta)$ for which that point has the coordinates $(0,0)$.

I just want to verify here, the transformation is given by $R = r - 1$ and $\Theta = \theta - \frac{\pi}{4}$, correct?

Answer 1

Hint

We can consider polar coordinates as vectors and then use vector subtraction