Question 122525
# 11
Using the conversion formulas that convert polar to rectangular, we have 



*[Tex \LARGE y=r\sin(\theta)] (since we're dealing with sine) and *[Tex \LARGE r=\sqrt{x^{2}+y^{2}}] 




*[Tex \LARGE r^{2}=x^{2}+y^{2}] Now square both sides of the second formula



 ------------------ Now let's manipulate *[Tex \LARGE r=\sin(\theta)]: 



*[Tex \LARGE r^2=r\sin(\theta)] Multiply both sides by r 



*[Tex \LARGE x^{2}+y^{2}=r\sin(\theta)] Replace *[Tex \LARGE r^{2}] with *[Tex \LARGE x^{2}+y^{2}]. Remember, *[Tex \LARGE r^{2}=x^{2}+y^{2}] 




*[Tex \LARGE x^{2}+y^{2}=y] Replace *[Tex \LARGE r\sin(\theta)] with *[Tex \LARGE y]. Remember, *[Tex \LARGE y=r\sin(\theta)] 




So the polar equation *[Tex \LARGE r=\sin(\theta)] converts to *[Tex \LARGE x^{2}+y^{2}=y] So the answer is A)