Find the Other Trig Values in Quadrant I sin(t)=15/17

$\sin (t) = \frac{15}{17}$

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.

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

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.

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

Replace the known values in the equation.

$Adjacent = \sqrt{{(17)}^{2} - {(15)}^{2}}$

Simplify inside the radical.

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

Adjacent $= \sqrt{289 - {(15)}^{2}}$

Raise $15$ to the power of $2$ .

Adjacent $= \sqrt{289 - 1 \cdot 225}$

Multiply $- 1$ by $225$ .

Adjacent $= \sqrt{289 - 225}$

Subtract $225$ from $289$ .

Adjacent $= \sqrt{64}$

Rewrite $64$ as $8^{2}$ .

Adjacent $= \sqrt{8^{2}}$

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

Adjacent $= 8$

Find the value of cosine.

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

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