?

Hello! I'd preface this by saying that I understand the concepts of cartesian and polar coordinates, but I am experiencing a major brain fart with regards to converting cartesian velocities to polar in relation to velocity fields.

I have attached an image from a video I was watching. What my brain is refusing to understand is how this can be the case.

Surely the i component of r is r*cos(theta). But here the video says that the i component multiplied by cos(theta) is the i component of x.

Something is just not clicking in my brain, and I'm sure it's completely obvious but nevertheless I am very confused.

For context, I am trying to derrive the polar forms of potential functions for a fluid velocity field. But this relies on me understanding that Vr = u*cos(theta), and not the other way around.

Can anyone maths my brain into order? Thanks.