Precalculus Examples

$(0.7, - 1.1)$

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.

$r = \sqrt{{(0.7)}^{2} + {(- 1.1)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

Tap for more steps...

Step 3.1

Raise $0.7$ to the power of $2$ .

$r = \sqrt{0.49 + {(- 1.1)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

Raise $- 1.1$ to the power of $2$ .

$r = \sqrt{0.49 + 1.21}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $0.49$ and $1.21$ .

$r = \sqrt{1.7}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Evaluate the root.

$r = 1.30384048$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 1.30384048$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = 1.30384048$

$θ = t a n^{- 1} (\frac{- 1.1}{0.7})$

Step 5

The inverse tangent of $- 1.\overline{571428}$ is $θ = 302.47119229 °$ .

$r = 1.30384048$

$θ = 302.47119229 °$

Step 6

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

$(1.30384048, 302.47119229 °)$