Question

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

(3, 3,4)

Answer 1

Solution

Relationship between Cartesian coordinates and Cylindrical coordinates is as follows:

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

$tan\theta=\frac yx$

$z=z$

Given

x=3

y=3

z=4

Hence

$r^2=3^2+3^2=18$

$r=\sqrt{18}=3\sqrt2$

$tan(\theta)=\frac{3}{3}=1$

$\theta=\frac{π}{4}$

$z=4$

The cylindrical coordinates are given by

$(3\sqrt2,\frac{π}{4},4)$ .