Question

How do you convert the point (3,-3, 7) from rectangular coordinates to cylindrical coordinates?

Answer 1

Cylindrical coordinates are `(3sqrt2,-pi/4,7)`

Explanation:

The relation between rectangular coordinates (in `3`-dimension) `(x,y,z)` and cylindrical coordinates `(r,phi,z)` is

`r=sqrt(x^2+y^2)`, `phi=tan^(-1)(y/x)` and `z=z`

As rectangular coordinates are `(3,-3,7)`, we have

`r=sqrt(3^2+(-3)^2)=sqrt(9+9)=sqrt18=3sqrt2`

`phi=tan^(-1)(-3/3)=tan^(-1)(-1)=-pi/4`

Hence, cylindrical coordinates are `(3sqrt2,-pi/4,7)`