Find the Cosine (-18,-24)

$(- 18, - 24)$

To find the $\cos (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 18, - 24)$ , draw the triangle between the three points $(0, 0)$ , $(- 18, 0)$ , and $(- 18, - 24)$ .

Opposite : $- 24$

Adjacent : $- 18$

Find the hypotenuse using Pythagorean theorem $c = \sqrt{a^{2} + b^{2}}$ .

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Raise $- 18$ to the power of $2$ .

$\sqrt{324 + {(- 24)}^{2}}$

Raise $- 24$ to the power of $2$ .

$\sqrt{324 + 576}$

Add $324$ and $576$ .

$\sqrt{900}$

Rewrite $900$ as $30^{2}$ .

$\sqrt{30^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$30$

$\cos (θ) = \frac{Adjacent}{Hypotenuse}$ therefore $\cos (θ) = \frac{- 18}{30}$ .

$\frac{- 18}{30}$

Simplify $\cos (θ)$ .

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Cancel the common factor of $- 18$ and $30$ .

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Factor $6$ out of $- 18$ .

$\cos (θ) = \frac{6 (- 3)}{30}$

Cancel the common factors.

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Factor $6$ out of $30$ .

$\cos (θ) = \frac{6 \cdot - 3}{6 \cdot 5}$

Cancel the common factor.

$\cos (θ) = \frac{6 \cdot - 3}{6 \cdot 5}$

Rewrite the expression.

$\cos (θ) = \frac{- 3}{5}$

Move the negative in front of the fraction.

$\cos (θ) = - \frac{3}{5}$

Approximate the result.

$\cos (θ) = - \frac{3}{5} \approx - 0.6$

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