Answer to Question #335777 in Calculus for Dhanush

Question

Find the cylindrical coordinates of the points where the cartesian coordinates are i)(3,3,4) ii) (√5,1,2)

Answer 1

$r^2=x^2+y^2$

$tan \phi=y/x$

z=z

1. x=3, y=3, z=4

$r= \sqrt{3^2+3^2}= \sqrt{18}$

$tan \phi =1$

$\phi =\pi/4$

z=4

So, the cylindric coordinates are ($\sqrt{18},\pi/4,4)$

2. $x=\sqrt{5}$ ,y=1, z=2

$r=\sqrt{\sqrt{5}^2+1^2}=\sqrt6$

$tan\phi=1/\sqrt{5}$

$\phi=\pi/7.5$

z=2

So, the cylindric coordinates are ($\sqrt6, \pi/7.5,2)$