Question

answer
\\(\cos e = \square\\)
\\(\sin f = \square\\)
\\(\cos e\\) and \\(\sin f\\) \\(\

$$\begin{aligned}&\\text{are equal}\\\\&\\text{are not equal}\\end{aligned}$$

\\)

Explanation:

Step1: Find cos E

In right triangle \( \triangle DEF \), \( \angle D = 90^\circ \), \( DE = 15 \), \( EF = 39 \), \( DF = 36 \), \( DE = 15 \). For \( \cos E \), in \( \triangle DEF \), \( \cos E=\frac{\text{adjacent to } E}{\text{hypotenuse}} \). The adjacent side to \( E \) is \( DE = 15 \), hypotenuse is \( EF = 39 \). So \( \cos E=\frac{15}{39}=\frac{5}{13} \).

Step2: Find sin F

For \( \sin F \), in \( \triangle DEF \), \( \sin F=\frac{\text{opposite to } F}{\text{hypotenuse}} \). The opposite side to \( F \) is \( DE = 15 \), hypotenuse is \( EF = 39 \). So \( \sin F=\frac{15}{39}=\frac{5}{13} \).

Step3: Compare cos E and sin F

Since \( \cos E=\frac{5}{13} \) and \( \sin F=\frac{5}{13} \), they are equal.

Answer:

\( \cos E = \frac{5}{13} \)
\( \sin F = \frac{5}{13} \)
\( \cos E \) and \( \sin F \) are equal