Question

consider △dfe. what are the inputs or outputs of the following trigonometric ratios? express the ratios in simplest terms. sin( ) = 4/5 cos(f) = tan(d) =

Explanation:

Step1: Recall sine ratio

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\sin(\text{?})=\frac{4}{5}$, since $\frac{20}{25}=\frac{4}{5}$, it's $\sin(F)$.

Step2: Recall cosine ratio

$\cos(F)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{15}{25}=\frac{3}{5}$.

Step3: Recall tangent ratio

$\tan(D)=\frac{\text{opposite}}{\text{adjacent}}=\frac{15}{20}=\frac{3}{4}$.

Answer:

$\sin(F)=\frac{4}{5}$, $\cos(F)=\frac{3}{5}$, $\tan(D)=\frac{3}{4}$