## Calculus 8th Edition

cylinder with radius $1$ and center $(0,1,0)$
We are given that $r=2 \sin \theta$ In the cylindrical coordinate system, we have $x=r \cos \theta \\ y=r \sin \theta \\z=z$ Conversion of rectangular to cylindrical coordinate system, we have $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$ Thus, we have $x^2+y^2=2y$ or, $x^2+y^2-2y=0$ or, $x^2+(y^2-2y+1)=1$ or, $x^2+(y-1)^2=1^2$ Hence, we get an equation of a cylinder with radius $1$ and center $(0,1,0)$ .