Answer
$(\frac{3}{2}, \frac{3\sqrt 3}{2},9) \Longrightarrow (3, \frac{\pi}{3},9) $.
Work Step by Step
We have $$ x=\frac{3}{2}, \quad y =\frac{3\sqrt 3}{2}, \quad z=9.$$
Now, we have
$$ r=\sqrt{x^2+y^2}=\sqrt{36/4}=3,$$
$$\theta =\tan^{-1}y/x=\tan^{-1}\frac{1}{\sqrt{3}}=\frac{\pi}{3},$$
$$ z=9.$$
So, $(\frac{3}{2}, \frac{3\sqrt 3}{2},9) \Longrightarrow (3, \frac{\pi}{3},9) $.
