Trigonometry Examples

$(- 1, 0)$

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.

$r = \sqrt{{(- 1)}^{2} + {(0)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

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Step 3.1

Raise $- 1$ to the power of $2$ .

$r = \sqrt{1 + {(0)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

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

$r = \sqrt{1 + 0}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $1$ and $0$ .

$r = \sqrt{1}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Any root of $1$ is $1$ .

$r = 1$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 1$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = 1$

$θ = t a n^{- 1} (\frac{0}{- 1})$

Step 5

The inverse tangent of $0$ is $θ = 0 °$ .

$r = 1$

$θ = 0 °$

Step 6

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

$(1, 0 °)$