Precalculus Examples

$(- 2, 9)$

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.

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

$θ = t a n^{- 1} (\frac{y}{x})$

Find the magnitude of the polar coordinate.

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

$r = \sqrt{4 + {(9)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Remove parentheses around $9$ .

$r = \sqrt{4 + 9^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

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

$r = \sqrt{4 + 81}$

$θ = t a n^{- 1} (\frac{y}{x})$

Add $4$ and $81$ .

$r = \sqrt{85}$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = \sqrt{85}$

$θ = t a n^{- 1} (\frac{y}{x})$

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

$r = \sqrt{85}$

$θ = t a n^{- 1} (\frac{9}{- 2})$

The inverse tangent of $- \frac{9}{2}$ is $θ = 282.5288077 °$ .

$r = \sqrt{85}$

$θ = 282.5288077 °$

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

$(\sqrt{85}, 282.5288077 °)$

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