SOLUTION: Write polar equation in rectangular form. r=6sin(theta)

If we draw the graph of that on polar graph paper. we make
a table of points:

  q | r
  0°|0.00
 15°|1.55
 30°|3.00
 45°|4.24
 60°|5.20
 75°|5.80
 90°|6.00
105°|5.80
120°|5.20
135°|4.24
150°|3.00
165°|1.55
180°|0.00

We get this circle:



When changing from one form to the other always draw this first:



We substitute for the sine first.
Looking at the triangle and remembering that
 



so substitute  for  first





Multiply both sides by r



Now use the Pythagorean theorem to substitute 
for 

  <-- answer

As a check let's graph it.

Get it in standard form:



Write x as (x-0)

Complethe square:
take half or -6, get -3
Square it, get 9
Add 9 to both sides:



Factor the trinomial in y:



That's a circle with center (0,3) and radius 3:



It graphs as the same circle, so we are right.

Edwin