Find the Trig Value sin(x)=8/17

$\sin (x) = \frac{8}{17}$

Step 1

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

$\sin (x) = \frac{opposite}{hypotenuse}$

Step 2

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

$Adjacent = \sqrt{{hypotenuse}^{2} - {opposite}^{2}}$

Step 3

Replace the known values in the equation.

$Adjacent = \sqrt{{(17)}^{2} - {(8)}^{2}}$

Step 4

Simplify inside the radical.

Raise $17$ to the power of $2$ .

Adjacent $= \sqrt{289 - {(8)}^{2}}$

Raise $8$ to the power of $2$ .

Adjacent $= \sqrt{289 - 1 \cdot 64}$

Multiply $- 1$ by $64$ .

Adjacent $= \sqrt{289 - 64}$

Subtract $64$ from $289$ .

Adjacent $= \sqrt{225}$

Rewrite $225$ as $15^{2}$ .

Adjacent $= \sqrt{15^{2}}$

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

Adjacent $= 15$

Step 5

Find the value of cosine.

Use the definition of cosine to find the value of $\cos (x)$ .

$\cos (x) = \frac{adj}{hyp}$