Trigonometry Examples

$(- 24, 10)$

Step 1

To find the $\cos (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 24, 10)$ , draw the triangle between the three points $(0, 0)$ , $(- 24, 0)$ , and $(- 24, 10)$ .

Opposite : $10$

Adjacent : $- 24$

Step 2

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

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Step 2.1

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

$\sqrt{576 + {(10)}^{2}}$

Step 2.2

Raise $10$ to the power of $2$ .

$\sqrt{576 + 100}$

Step 2.3

Add $576$ and $100$ .

$\sqrt{676}$

Step 2.4

Rewrite $676$ as $26^{2}$ .

$\sqrt{26^{2}}$

Step 2.5

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

$26$

Step 3

$\cos (θ) = \frac{Adjacent}{Hypotenuse}$ therefore $\cos (θ) = \frac{- 24}{26}$ .

$\frac{- 24}{26}$

Step 4

Simplify $\cos (θ)$ .

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Step 4.1

Cancel the common factor of $- 24$ and $26$ .

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Step 4.1.1

Factor $2$ out of $- 24$ .

$\cos (θ) = \frac{2 (- 12)}{26}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $26$ .

$\cos (θ) = \frac{2 \cdot - 12}{2 \cdot 13}$

Step 4.1.2.2

Cancel the common factor.

$\cos (θ) = \frac{2 \cdot - 12}{2 \cdot 13}$

Step 4.1.2.3

Rewrite the expression.

$\cos (θ) = \frac{- 12}{13}$

Step 4.2

Move the negative in front of the fraction.

$\cos (θ) = - \frac{12}{13}$

Step 5

Approximate the result.

$\cos (θ) = - \frac{12}{13} \approx - 0.\overline{923076}$