Answer
$(4, \dfrac{\pi}{6}, -1)$
and
$(5, -36.87^{\circ}, 2)$ or, $(5, \arctan (\dfrac{-3}{4}), 2)$
Work Step by Step
In the cylindrical coordinate system, we have $x=r \cos \theta \\ y=r \sin \theta \\z=z$
The conversion of rectangular to cylindrical coordinate system gives:
$r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
$r=\sqrt{(2\sqrt3)^2+2^2} \implies r= 4$
Here, $ \theta=\tan^{-1} (\dfrac{2}{2 \sqrt 3})$
and $\theta=\arctan (\dfrac{2}{2 \sqrt 3})=\dfrac{\pi}{6}$
Therefore, $(4, \dfrac{\pi}{6}, -1)$
b) $r=\sqrt{4^2+(-3)^2} =5$
Conversion of rectangular to cylindrical coordinate system gives:
$r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$
$\theta=\arctan (\dfrac{-3}{4}) =-36.87^{\circ}$
Hence, the rectangular coordinates are: $(5, -36.87^{\circ}, 2)$ or, $(5, \arctan (\dfrac{-3}{4}), 2)$
