Precalculus Examples

$(3, π)$

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.

$r = \sqrt{{(3)}^{2} + {(π)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Raise $3$ to the power of $2$ .

$r = \sqrt{9 + π^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = \sqrt{9 + π^{2}}$

$θ = t a n^{- 1} (\frac{π}{3})$

Step 5

The inverse tangent of $\frac{π}{3}$ is $θ = 46.32070377 °$ .

$r = \sqrt{9 + π^{2}}$

$θ = 46.32070377 °$

Step 6

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

$(\sqrt{9 + π^{2}}, 46.32070377 °)$