# How do you convert the Cartesian coordinates (1 , sqrt(3)) to polar coordinates?

$r = 2$ and $\theta = \frac{\pi}{3}$ OR simply
$\left(2 , \frac{\pi}{3}\right)$

#### Explanation:

give $x = 1$ and $y = \sqrt{3}$

$r = \sqrt{{x}^{2} + {y}^{2}} = \sqrt{{1}^{2} + {\sqrt{3}}^{2}} = \sqrt{4} = 2$

$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right) = {\tan}^{-} 1 \left(\frac{\sqrt{3}}{1}\right) = \frac{\pi}{3}$

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The text passage contains a mathematical question about converting Cartesian coordinates to polar coordinates, and it provides the answer to this question.
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First, describe the content structure you found in 1-2 sentences.

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# How do you convert the Cartesian coordinates (1 , sqrt(3)) to polar coordinates?

$r = 2$ and $\theta = \frac{\pi}{3}$ OR simply
$\left(2 , \frac{\pi}{3}\right)$

#### Explanation:

give $x = 1$ and $y = \sqrt{3}$

$r = \sqrt{{x}^{2} + {y}^{2}} = \sqrt{{1}^{2} + {\sqrt{3}}^{2}} = \sqrt{4} = 2$

$\theta = {\tan}^{-} 1 \left(\frac{y}{x}\right) = {\tan}^{-} 1 \left(\frac{\sqrt{3}}{1}\right) = \frac{\pi}{3}$

God bless America !!!
user
The text passage contains a mathematical question about converting Cartesian coordinates to polar coordinates, and it provides the answer to this question.

TYPE: SINGLE_QUESTION_WITH_ANSWER