Find the Trig Value cos(x)=12/13

$\cos (x) = \frac{12}{13}$

Step 1

Use the definition of cosine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

$\cos (x) = \frac{adjacent}{hypotenuse}$

Step 2

Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.

$Opposite = \sqrt{{hypotenuse}^{2} - {adjacent}^{2}}$

Step 3

Replace the known values in the equation.

$Opposite = \sqrt{{(13)}^{2} - {(12)}^{2}}$

Step 4

Simplify inside the radical.

Raise $13$ to the power of $2$ .

Opposite $= \sqrt{169 - {(12)}^{2}}$

Raise $12$ to the power of $2$ .

Opposite $= \sqrt{169 - 1 \cdot 144}$

Multiply $- 1$ by $144$ .

Opposite $= \sqrt{169 - 144}$

Subtract $144$ from $169$ .

Opposite $= \sqrt{25}$

Rewrite $25$ as $5^{2}$ .

Opposite $= \sqrt{5^{2}}$

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

Opposite $= 5$

Step 5

Find the value of sine.

Use the definition of sine to find the value of $\sin (x)$ .

$\sin (x) = \frac{opp}{hyp}$