To change from either polar form to rectangular form, or from
rectangular to polar form, always begin by drawing the graph
below, and out beside it write out the four equations, the 
three basic trig ratios and the Pythagorean theorem equation:



To change 



Solve (2) for x by clearing  of fractions
by multiplying both sides by r: 
So replace  by 



Solve (1) for y by clearing  of fractions
by multiplying both sides by r: 
So replace  by 



Solve for r by first factoring out r on the left:





----------------------------------- 

 





Always substitute for the trig functions first, and for r last:

Substitute  for 





Clear of fractions by multiplying both sides by r:



Now use (4) to replace  by 



---------------------



Clear of fractions by multiplying both sides by 





Again, always substitute for the trig functions first, and for r last: 

Use (2) to substitute for 



Distribute to remove the parentheses on the left side:



Solve (4) for :    and replace
r by that:



Isolate the square root term on the left by adding x to both sides:



Square both sides







Simplify by subtracting  from both sides:



Edwin
-----------------------------------------------------------
[BTW, this symbol  is not "data", it's the Greek letter
"theta".  It stands for the angle in the graph above.]