Trigonometry Examples

(0, 1)

$(0, 1)$

Step 1

Convert from rectangular coordinates

(x, y)

$(x, y)$ to polar coordinates

(r, θ)

$(r, θ)$ using the conversion formulas.

r = \sqrt{x^{2} + y^{2}}

$r = \sqrt{x^{2} + y^{2}}$

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

Step 2

Replace

x

$x$ and

y

$y$ with the actual values.

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

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

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

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Step 3.1

Raising

0

$0$ to any positive power yields

0

$0$ .

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

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

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

One to any power is one.

r = \sqrt{0 + 1}

$r = \sqrt{0 + 1}$

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add

0

$0$ and

1

$1$ .

r = \sqrt{1}

$r = \sqrt{1}$

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Any root of

1

$1$ is

1

$1$ .

r = 1

$r = 1$

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

r = 1

$r = 1$

θ = t a n^{- 1} (\frac{y}{x})

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

Replace

x

$x$ and

y

$y$ with the actual values.

r = 1

$r = 1$

θ = t a n^{- 1} (\frac{1}{0})

$θ = t a n^{- 1} (\frac{1}{0})$

Step 5

The inverse tangent of Undefined is

θ = 90 °

$θ = 90 °$ .

r = 1

$r = 1$

θ = 90 °

$θ = 90 °$

Step 6

This is the result of the conversion to polar coordinates in

(r, θ)

$(r, θ)$ form.

(1, 90 °)

$(1, 90 °)$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$