Trigonometry Examples

$(4, 55)$

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.

$r = \sqrt{{(4)}^{2} + {(55)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

Tap for more steps...

Step 3.1

Raise $4$ to the power of $2$ .

$r = \sqrt{16 + {(55)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

Raise $55$ to the power of $2$ .

$r = \sqrt{16 + 3025}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $16$ and $3025$ .

$r = \sqrt{3041}$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = \sqrt{3041}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = \sqrt{3041}$

$θ = t a n^{- 1} (\frac{55}{4})$

Step 5

The inverse tangent of $\frac{55}{4}$ is $θ = 85.8403577 °$ .

$r = \sqrt{3041}$

$θ = 85.8403577 °$

Step 6

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

$(\sqrt{3041}, 85.8403577 °)$