When converting between rectangular and polar form,
either to or from, always draw this first:

 

Then write down the trig functions for the triangle:




Since we are converting from rectangular to polar, we solve
each of those for x and y.  

[If we were converting from polar to rectangular, we would
solve each for r.]









Substitute for x and y:





Simplify and if reasonably easy, solve for r or r²:







We can even make it simpler by substituting

 for 





Edwin