Question

Find the cylindrical coordinates of the points where the Cartesian coordinates are

i)( 6,6,8)
ii) ( √2,1,1)

Answer 1

Find the cylindrical coordinates of the points where the Cartesian coordinates are

i)( 6,6,8)

ii) ( √2,1,1)

Solution:

relation between cartesian coordinate and cylindrical coordinate

$r^2=x^2+y^2\newline tan(\theta)=y/x\newline z=z$

$x=6,y=6,z=8\newline r^2=(x^2+y^2)\implies r= 6\sqrt{2}\newline \theta=\pi/4\newline z=8\newline \newline Answer : (6\sqrt{2},\pi/4,8)$

$x=\sqrt2,y=1,z=1\newline r^2=(x^2+y^2)\implies r= \sqrt{3}\newline \theta=0.615rad\newline z=1\newline$

$Answer : (\sqrt{3},0.615,1)$

*angle is given in radian