Convert to Polar Coordinates (-1,-1.73)

$(- 1, - 1.73)$

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.

$r = \sqrt{{(- 1)}^{2} + {(- 1.73)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Find the magnitude of the polar coordinate.

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Raise $- 1$ to the power of $2$ .

$r = \sqrt{1 + {(- 1.73)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Raise $- 1.73$ to the power of $2$ .

$r = \sqrt{1 + 2.9929}$

$θ = t a n^{- 1} (\frac{y}{x})$

Add $1$ and $2.9929$ .

$r = \sqrt{3.9929}$

$θ = t a n^{- 1} (\frac{y}{x})$

Evaluate the root.

$r = 1.99822421$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 1.99822421$

$θ = t a n^{- 1} (\frac{y}{x})$

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

$r = 1.99822421$

$θ = t a n^{- 1} (\frac{- 1.73}{- 1})$

The inverse tangent of $1.73$ is $θ = 239.97059823 °$ .

$r = 1.99822421$

$θ = 239.97059823 °$

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

$(1.99822421, 239.97059823 °)$

Convert to Polar Coordinates (-1,-1.73)

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