# The equivalent polar coordinates for the given rectangular coordinates. A rectangular coordinate is given as (0, -3).

The equivalent polar coordinates for the given rectangular coordinates.
A rectangular coordinate is given as (0, -3).
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saiyansruleA

Conversion formula for coordinate systems are given as:
a) From polar to rectangular:
$x=r\mathrm{cos}\theta$
$y=r\mathrm{sin}\theta$
b) From rectangular to polar:
$r=±\sqrt{{x}^{2}+{y}^{2}}$
$\mathrm{cos}\theta =\frac{x}{r};\mathrm{sin}\theta =\frac{y}{r};\mathrm{tan}\theta =\frac{x}{y}$
Here $x=0,y=-3$
Converting into equivalent polar coordinates:
$r=±\sqrt{{x}^{2}+{y}^{2}}$
$⇒r=±\sqrt{{0}^{2}+{\left(-3\right)}^{2}}$
$⇒r=±3$
$\mathrm{cos}\theta =\frac{x}{r}=\frac{0}{3}=0$ {Taking positive value of r}
$⇒\theta ={90}^{\circ },{270}^{\circ }$
$\mathrm{sin}\theta =\frac{y}{r}=\frac{-3}{3}=1$
$⇒\theta ={270}^{\circ }$
Hence, desired equivalent polar coordinates would be $\left(3,{270}^{\circ }\right)$