Given angle and distance, finding $X,Y$ coordinates in an unusual coordinate system

Question

I have a coordinate system in which $+Y$ is down, $-Y$ is up, $+X$ is right, $-X$ is left. Positive angles are clockwise, negative is counter-clockwise, and the $0$ degree line is straight down.

Using this coordinate system, I want to convert any angle/distance into $X, Y$ values.

I know how to convert polar to rectangular but I can't seem to get it to work for this coordinate system.

Thanks in advance.

Answer 1

Assuming you mean polar form in this coordinate system and taking distance from origin.

$r\cos\theta=y$

$r\sin\theta=-x$

Why don't you make a diagram and see it? Note that the distance is always positive.