Conversion formula for coordinate systems are given as:

a) From polar to rectangular:

\(\displaystyle{x}={r} \cos{\theta}\)

\(\displaystyle{y}={r} \sin{\theta}\)

b) From rectangular to polar:

\(\displaystyle{r}=\pm\sqrt{{{x}^{2}+{y}^{2}}}\)

\(\displaystyle \cos{\theta}=\frac{x}{{r}}; \sin{\theta}=\frac{y}{{r}}; \tan{\theta}=\frac{x}{{y}}\)

Here \(\displaystyle{x}={0},{y}=-{3}\)

Converting into equivalent polar coordinates:

\(\displaystyle{r}=\pm\sqrt{{{x}^{2}+{y}^{2}}}\)

\(\displaystyle\Rightarrow{r}=\pm\sqrt{{{0}^{2}+{\left(-{3}\right)}^{2}}}\)

\(\displaystyle\Rightarrow{r}=\pm{3}\)

\(\displaystyle \cos{\theta}=\frac{x}{{r}}=\frac{0}{{3}}={0}\) {Taking positive value of r}

\(\displaystyle\Rightarrow\theta={90}^{\circ},{270}^{\circ}\)

\(\displaystyle \sin{\theta}=\frac{y}{{r}}=\frac{{-{3}}}{{3}}={1}\)

\(\displaystyle\Rightarrow\theta={270}^{\circ}\)

Hence, desired equivalent polar coordinates would be \(\displaystyle{\left({3},{270}^{\circ}\right)}\)