document.write( "Question 1204941: Convert the given polar equation to a Cartesian equation. (Use the following as necessary: x and y.)
\n" ); document.write( "r = 4 sin(𝜃) \n" ); document.write( "
Algebra.Com's Answer #841501 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The other tutors have great answers. I'll extend their scratch work to complete the square for the y term, and use it to determine the center and radius of this circle.\r
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\n" ); document.write( "\n" ); document.write( "In the fourth step shown below, I add and subtract 4.
\n" ); document.write( "The 4 comes from taking half of the y coefficient, and then squaring it.\r
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\n" ); document.write( "\n" ); document.write( "x^2 + y^2 = 4y
\n" ); document.write( "x^2 + y^2 - 4y = 0
\n" ); document.write( "x^2 + (y^2 - 4y) = 0
\n" ); document.write( "x^2 + (y^2 - 4y + 4 - 4) = 0
\n" ); document.write( "x^2 + (y^2 - 4y + 4) - 4 = 0
\n" ); document.write( "x^2 + (y-2)^2 - 4 = 0
\n" ); document.write( "x^2 + (y-2)^2 = 4\r
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\n" ); document.write( "\n" ); document.write( "Compare that to the circle template (x-h)^2 + (y-k)^2 = r^2
\n" ); document.write( "We determine that h = 0, k = 2, r = 2
\n" ); document.write( "This circle has its center at (h,k) = (0,2) and has radius r = 2.
\n" ); document.write( "Desmos can be used to confirm the answer
\n" ); document.write( "https://www.desmos.com/calculator/os2lf1m92p
\n" ); document.write( "Click the wrench icon in the upper right corner to go from cartesian mode to polar mode. \r
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\n" ); document.write( "\n" ); document.write( "Even though it appears your teacher may not be asking for the circle's center and radius, it's still good practice to be able to find it.
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