Question

How do you change `(2sqrt(3),2,-1)`   from rectangular to cylindrical coordinates?

Answer 1

Hello !

First, you have to calculate the radius `r = sqrt{x^2+y^2} = sqrt{12+4}=4`.

Second, you know that `x=r\cos(\theta)` and `y=r\sin(\theta)`, therefore, `\cos(\theta) = \frac{\sqrt{3}}{2}` and `y=\frac{1}{2}`. So, `\theta = \frac{\pi}{6}` (modulo `2\pi`).

Conclusion, the cylindrical coordinates are `(4,\frac{\pi}{6},-1)`.