Trigonometry Examples

$(0, - 3)$

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.

$r = \sqrt{{(0)}^{2} + {(- 3)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

Tap for more steps...

Step 3.1

Raising $0$ to any positive power yields $0$ .

$r = \sqrt{0 + {(- 3)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

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

$r = \sqrt{0 + 9}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $0$ and $9$ .

$r = \sqrt{9}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Rewrite $9$ as $3^{2}$ .

$r = \sqrt{3^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.5

Pull terms out from under the radical, assuming positive real numbers.

$r = 3$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 3$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = 3$

$θ = t a n^{- 1} (\frac{- 3}{0})$

Step 5

The inverse tangent of Undefined is $θ = 270 °$ .

$r = 3$

$θ = 270 °$

Step 6

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

$(3, 270 °)$