Precalculus Examples

$(2, 5)$

Step 1

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

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

$θ = t a n^{- 1} (\frac{y}{x})$

Step 2

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

$r = \sqrt{{(2)}^{2} + {(5)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

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Step 3.1

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

$r = \sqrt{4 + {(5)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

Raise $5$ to the power of $2$ .

$r = \sqrt{4 + 25}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $4$ and $25$ .

$r = \sqrt{29}$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = \sqrt{29}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = \sqrt{29}$

$θ = t a n^{- 1} (\frac{5}{2})$

Step 5

The inverse tangent of $\frac{5}{2}$ is $θ = 68.19859051 °$ .

$r = \sqrt{29}$

$θ = 68.19859051 °$

Step 6

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

$(\sqrt{29}, 68.19859051 °)$