# How do you convert (5.7, -1.2)  into polar coordinates?

Dec 30, 2015

If $\left(x , y\right)$ is are the coordinates of a point in the rectangular coordinate system then we convert it into polar form as follows.

Let the polar form of $\left(x , y\right)$ be $\left(r , \theta\right)$. Where $r$ is the principal square root of sum of squares of the coordinates of the point in rectangular system i.e $r = \sqrt{{x}^{2} + {y}^{2}}$ and $\theta$ is the inverse tangent of the ratio from y coordinate to x coordinate in the rectangular coordinate system i.e $\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right)$.
Here $x = 5.7$ and $y = - 1.2$.
$\implies r = \sqrt{{\left(5.7\right)}^{2} + {\left(- 1.2\right)}^{2}} = \sqrt{32.49 + 1.44} = \sqrt{33.93}$
Also, $\theta = {\tan}^{-} 1 \left(- \frac{1.2}{5.7}\right) = {\tan}^{-} 1 \left(- \frac{12}{57}\right) = {\tan}^{-} 1 \left(- \frac{4}{19}\right)$.

Hence the polar form of the given number is $\left(\sqrt{33.93} , {\tan}^{-} 1 \left(- \frac{4}{19}\right)\right)$.