Question

b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2)

i) )8,6,6(
ii) ( 1,1,2 )

Answer 1

Correspondence between cylindrical $(\rho,\phi,z)$ and Cartesian ($x,y,z)$ is

$\rho=\sqrt{x^2+y^2},\phi=\arctan( y/x), z=z$ then

i) $\rho=\sqrt{8^2+6^2}=10, \phi=\arctan(6/8)\approx 37^0,z=6$

ii)$\rho=\sqrt{1^2+1^2}=\sqrt{2},\phi=\arctan1=45^0,z=2$