Trigonometry Examples

$(0, - 9)$

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.

$r = \sqrt{{(0)}^{2} + {(- 9)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

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Step 3.1

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

$r = \sqrt{0 + {(- 9)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

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

$r = \sqrt{0 + 81}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $0$ and $81$ .

$r = \sqrt{81}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Rewrite $81$ as $9^{2}$ .

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

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.5

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

$r = 9$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 9$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = 9$

$θ = t a n^{- 1} (\frac{- 9}{0})$

Step 5

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

$r = 9$

$θ = 270 °$

Step 6

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

$(9, 270 °)$