Question

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

Explanation:

Step1: Find the hypotenuse \( WX \)

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( a = 56 \), \( b=33 \).
\( WX=\sqrt{56^{2}+33^{2}}=\sqrt{3136 + 1089}=\sqrt{4225}=65 \)

Step2: Calculate \( \sin(X) \)

\( \sin(X)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{WY}{WX} \)
\( \sin(X)=\frac{56}{65} \)

Step3: Calculate \( \cos(X) \)

\( \cos(X)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{XY}{WX} \)
\( \cos(X)=\frac{33}{65} \)

Step4: Calculate \( \tan(X) \)

\( \tan(X)=\frac{\text{opposite}}{\text{adjacent}}=\frac{WY}{XY} \)
\( \tan(X)=\frac{56}{33} \)

Answer:

\(\sin(X)=\frac{56}{65}\), \(\cos(X)=\frac{33}{65}\), \(\tan(X)=\frac{56}{33}\)