Translation to plot line with hough transform when using polar coordinates

I have a bit of trouble understanding how lines are plotted after doing a Hough Transform using polar coordinates.

On the OpenCV example they do it like this:

a = math.cos(theta)
b = math.sin(theta)
x0 = a * rho
y0 = b * rho
pt1 = (int(x0 + 1000*(-b)), int(y0 + 1000*(a)))
pt2 = (int(x0 - 1000*(-b)), int(y0 - 1000*(a)))

I understand that they are taking two points far apart on the same line, but I have trouble understanding the "projection"/ multiplication by the sin for the x point and the cos for the y point.

Can anyone enlighten me?

Definitions of r and theta are as shown.

So, the blue line directional unit vector V is ( cos(theta), sin(theta) ),
and one point on the line is given as <code>r * V</code> (In your description, this is (x0,y0) ).

Points on the line can be obtained by moving along the line from this point.
The along directional unit vector U (which is perpendicular to V) , is ( -sin(theta), cos(theta) ) or ( sin(theta), -cos(theta) ).

So, points on the line is :

<code>r * V + k * U</code>

where, value of the scalar k is arbitrary amount of movement. (In your description, used k values are 1000 and -1000)

Therefore, short answer for

> the sin for the x point and the cos for the y

is, U : the unit directional vector along the line.