Find the Trig Value tan(x)=3/4

$\tan (x) = \frac{3}{4}$

Step 1

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

$\tan (x) = \frac{opposite}{adjacent}$

Step 2

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

$Hypotenuse = \sqrt{{opposite}^{2} + {adjacent}^{2}}$

Step 3

Replace the known values in the equation.

$Hypotenuse = \sqrt{{(3)}^{2} + {(4)}^{2}}$

Step 4

Simplify inside the radical.

Raise $3$ to the power of $2$ .

Hypotenuse $= \sqrt{9 + {(4)}^{2}}$

Raise $4$ to the power of $2$ .

Hypotenuse $= \sqrt{9 + 16}$

Add $9$ and $16$ .

Hypotenuse $= \sqrt{25}$

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

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

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

Hypotenuse $= 5$

Step 5

Find the value of sine.

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

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