Question

express the trig ratios as fractions in simplest terms. answer attempt 1 out of 2 $\sin d =$ $\cos c =$ $\sin d$ and $\cos c$

Explanation:

Step1: Recall the definition of sine and cosine

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\)

Step2: Find \(\sin D\)

For \(\angle D\), the opposite side to \(\angle D\) is \(BC = 33\) and the hypotenuse \(DC=55\). So \(\sin D=\frac{BC}{DC}=\frac{33}{55}\). Simplify \(\frac{33\div11}{55\div11}=\frac{3}{5}\)

Step3: Find \(\cos C\)

For \(\angle C\), the adjacent side to \(\angle C\) is \(BC = 33\) and the hypotenuse \(DC = 55\). So \(\cos C=\frac{BC}{DC}=\frac{33}{55}\). Simplify \(\frac{33\div11}{55\div11}=\frac{3}{5}\)

Answer:

\(\sin D=\frac{3}{5}\)
\(\cos C=\frac{3}{5}\)