Trigonometry Examples

$(0, - 2)$

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.

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

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

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Step 3.1

Raising

$0$ to any positive power yields

$0$ .

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

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

Raise

$- 2$ to the power of

$2$ .

$r = \sqrt{0 + 4}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add

$0$ and

$4$ .

$r = \sqrt{4}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Rewrite

$4$ as

$2^{2}$ .

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

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.5

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

$r = 2$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 2$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

Replace

$x$ and

$y$ with the actual values.

$r = 2$

$θ = t a n^{- 1} (\frac{- 2}{0})$

Step 5

The inverse tangent of Undefined is

$θ = 270 °$ .

$r = 2$

$θ = 270 °$

Step 6

This is the result of the conversion to polar coordinates in

$(r, θ)$ form.

$(2, 270 °)$