Question

find the sine, cosine, and tangent of ∠q. simplify your answers and write them as proper fractions, improper fractions, or whole numbers. sin(q) = cos(q) = tan(q) =

Explanation:

Step1: Find side QR via Pythagoras

$$QR = \sqrt{QP^2 - RP^2} = \sqrt{65^2 - 56^2} = \sqrt{4225 - 3136} = \sqrt{1089} = 33$$

Step2: Calculate sin(Q) (opp/hyp)

$$\sin(Q) = \frac{RP}{QP} = \frac{56}{65}$$

Step3: Calculate cos(Q) (adj/hyp)

$$\cos(Q) = \frac{QR}{QP} = \frac{33}{65}$$

Step4: Calculate tan(Q) (opp/adj)

$$\tan(Q) = \frac{RP}{QR} = \frac{56}{33}$$

Answer:

$\sin(Q) = \frac{56}{65}$
$\cos(Q) = \frac{33}{65}$
$\tan(Q) = \frac{56}{33}$