# Find a set of polar coordinates for the point for which the rectangular coordinates are given. Choose the polar coordinates where r is positive and 0<=theta<=pi (5sqrt3,5)

Find a set of polar coordinates for the point for which the rectangular coordinates are given. Choose the polar coordinates where r is positive and $0\le \theta \le \pi \left(5\sqrt{3},5\right)$
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$\left(5\sqrt{3},5\right)$ $\to$ rectangular coordinates
$xy$ Polar coordinates $\left(r,\theta \right)$
$r=\sqrt{{x}^{2}+{y}^{2}},$
$\theta ={\mathrm{tan}}^{-1}\left[\frac{y}{x}\right]$
$r={\sqrt{5\sqrt{3}}}^{2}+{5}^{2}=\sqrt{25\cdot 3+25}$
$r=\sqrt{100}=10$
$\theta ={\mathrm{tan}}^{-1}\left[\frac{5}{5\sqrt{3}}\right]={\mathrm{tan}}^{-1}\left[\frac{1}{\sqrt{3}}\right]$
$\theta ={30}^{o}$
$\left(r,\theta \right)=\left(10,{30}^{o}\right)=\left(10,\frac{\pi }{6}\right)$