please help with polar coordinates. Describe the given region in polar coordinates. The region enclosed by the semicircle x^2 + y^2 = 2y, y = 0 The solution ends up being r=2sin(theta), 0

Question

please help with polar coordinates.
Describe the given region in polar coordinates.  
The region enclosed by the semicircle x^2 + y^2 = 2y, y >= 0

The solution ends up being r=2sin(theta), 0<(theta)<pi/2, 0<=r<2sin(theta)


But how did they arrive at this solution?  medal given to whoever helps.  Thanks!

fifciol · Answer

first equation of circle
x^2-2y +1-1 +y^2=0
(x-1)^2+y^2=1
do you understand this ?

anonymous · Answer

you moved the y^2 over? where did the 1 and -1 come from

anonymous · Answer

*2y not y^2

fifciol · Answer

I added 1 and -1 so I effectively added 0 which doesn't change the expression but it helps to get a nice (y-1)^2 remember:
$$y^2-2y+1=(y-1)^2$$
there should be in my first post 
$$(y-1)^2+x^2=1$$
not x-1

anonymous · Answer

I thought you would substitute x=rcostheta and y=rsintheta into the equation x^2+y^2 = 2y?

fifciol · Answer

No, we're supposed to draw it first to determine the region. Now it's easy to do. We have a circle with center(0,1) and radius r do you agree?

fifciol · Answer

radius 1 *

anonymous · Answer

yes

fifciol · Answer

you have to describe every point on that circumference using r and theta

fifciol · Answer

sorry theta is wrong i'll type this out

anonymous · Answer

ok

fifciol · Answer

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fifciol · Answer

you see now the radius is a function of theta .can you describe the radius in terms of theta?

fifciol · Answer

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