Find the Trig Value sin(x)=7/25

$\sin (x) = \frac{7}{25}$

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.

$Adjacent = \sqrt{{(25)}^{2} - {(7)}^{2}}$

Step 4

Simplify inside the radical.

Raise $25$ to the power of $2$ .

Adjacent $= \sqrt{625 - {(7)}^{2}}$

Raise $7$ to the power of $2$ .

Adjacent $= \sqrt{625 - 1 \cdot 49}$

Multiply $- 1$ by $49$ .

Adjacent $= \sqrt{625 - 49}$

Subtract $49$ from $625$ .

Adjacent $= \sqrt{576}$

Rewrite $576$ as $24^{2}$ .

Adjacent $= \sqrt{24^{2}}$

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

Adjacent $= 24$

Step 5

Find the value of cosine.

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

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