How do you convert the polar equation #r=2sintheta# into rectangular form?

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Answer 1 · 2016-11-19T02:50:30

Please see the explanation.

Multiply both sides by r:

#r^2 = 2rsin(theta)#

Substitute #x^2 + y^2# for #r^2#

#x^2 + y^2 = 2rsin(theta)#

Substitute y for #rsin(theta)#

#x^2 + y^2 = 2y#

Add #k^2 - 2y# to both sides:

#x^2 + y^2 - 2y + k^2 = k^2#

#k = 1# completes the square:

#x^2 + (y - 1)^2 = 1^2#

Insert a zero in the x term:

#(x - 0)^2 + (y - 1)^2 = 1^2#

Standard form for the equation of a circle with a center of #(0,1)# and a radius of 1.