# From polar coordinates to heliocentric ecliptic coordinates

## Main Question or Discussion Point

So I've calculated the polar coordinates of a planet, with the sun at the origin and the x-axis being the striped line going from the sun towards point P.

Now I have to convert these polar coordinates to heliocentric ecliptic coordinates. To do this, I have to convert to cartesian coordinates first and then rotate the plane of reference so that the x-axis will point towards $$\Upsilon$$. This is the answer:

Converting to cartesian coordinates is easy, but then I'm lost. Could anyone tell me how exactly I go from $$x = r \cdot \cos{v}$$ to $$(6)$$?