Converting the coordinates of a point to cylindrical coordinates with positive values.

Question

I'm trying to convert the coordinates of point $(x,y,z) = (-2,-1,0)$ to cylindrical coordinates, with positive values for $\theta$ and $r$.

I know that:

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

so...

$r = \sqrt(5)$

And:

$\theta = arctan(y/x)$

so...

$\theta = arctan(1/2)$

which yields the cylindrical coordinates of...

$r = \sqrt(5)$

$\theta = arctan(1/2)$

$z = 0$

But apparently this is incorrect? Am I doing something wrong?

Answer 1

Your $r$ is correct.

Your $\theta $ should be in he third quadrant and have the same tangent as $1/2$

Thus it is $$\theta = \arctan (1/2) + \pi $$