Precalculus Examples

$(- 9, - 7)$

Convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, θ)$ using the conversion formulas.

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

$θ = t a n^{- 1} (\frac{y}{x})$

Replace $x$ and $y$ with the actual values.

$r = \sqrt{{(- 9)}^{2} + {(- 7)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Find the magnitude of the polar coordinate.

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Raise $- 9$ to the power of $2$ .

$r = \sqrt{81 + {(- 7)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Raise $- 7$ to the power of $2$ .

$r = \sqrt{81 + 49}$

$θ = t a n^{- 1} (\frac{y}{x})$

Add $81$ and $49$ .

$r = \sqrt{130}$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = \sqrt{130}$

$θ = t a n^{- 1} (\frac{y}{x})$

Replace $x$ and $y$ with the actual values.

$r = \sqrt{130}$

$θ = t a n^{- 1} (\frac{- 7}{- 9})$

The inverse tangent of $\frac{7}{9}$ is $θ = 217.87498365 °$ .

$r = \sqrt{130}$

$θ = 217.87498365 °$

This is the result of the conversion to polar coordinates in $(r, θ)$ form.

$(\sqrt{130}, 217.87498365 °)$

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