Convert circle from polar to cartesian form

[f1player]

Convert r = 2 sin (theta) into cartesian form:

It looks simple, but I can't do it

Here's what I did:

root(x^2 + y^2) = 2y/r, since y = r sin(theta)

So: 2y = root(x^2 + y^2) * root(x^2 + y^2)

2y = x^2 + y^2

and what now??

I know from calculator that the answer should be x^2 +(y-1)^2 = 1 with centre at (0,1).

 

[arthur ohlsten]

if we plot R=2Sin@ we obtain a circle of radius 1 centered at 0,1
or we have x^2+[y-1]^2=1


convert R=2Sin@ where:
x=Rcos@
y=Rsin@
R=sqrt[x^2+y^2]

R=2Sin@ MULTIPLY BOTH SIDES BY R
R^2=2Rsin@ substitute
x^2+y^2=2y subtract 2y from each side
x^2+y^2-2y = 0 complete the square
x^2+[y^2-2y+1]=1
x^2+[y-1]^2=1 answer

Arthur

 

[f1player]

Cheers