Trigonometry Examples

$(4.7, 4.2)$

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.

$r = \sqrt{{(4.7)}^{2} + {(4.2)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3

Find the magnitude of the polar coordinate.

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Step 3.1

Raise $4.7$ to the power of $2$ .

$r = \sqrt{22.09 + {(4.2)}^{2}}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.2

Raise $4.2$ to the power of $2$ .

$r = \sqrt{22.09 + 17.64}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.3

Add $22.09$ and $17.64$ .

$r = \sqrt{39.73}$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 3.4

Evaluate the root.

$r = 6.3031738$

$θ = t a n^{- 1} (\frac{y}{x})$

$r = 6.3031738$

$θ = t a n^{- 1} (\frac{y}{x})$

Step 4

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

$r = 6.3031738$

$θ = t a n^{- 1} (\frac{4.2}{4.7})$

Step 5

The inverse tangent of $0.89361702$ is $θ = 41.784516 °$ .

$r = 6.3031738$

$θ = 41.784516 °$

Step 6

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

$(6.3031738, 41.784516 °)$