Question

express the trig ratios as fractions in simplest terms.
answer attempt 1 out of 2
\\(\sin k = \square\\)
\\(\cos j = \square\\)
\\(\sin k\\) and \\(\cos j\\)

Explanation:

Step1: Recall sine definition

For an acute angle in a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$.
For $\angle K$, opposite side is $39$, hypotenuse is $65$.
$\sin K = \frac{39}{65}$
Simplify: $\frac{39\div13}{65\div13} = \frac{3}{5}$

Step2: Recall cosine definition

For an acute angle in a right triangle, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$.
For $\angle J$, adjacent side is $39$, hypotenuse is $65$.
$\cos J = \frac{39}{65}$
Simplify: $\frac{39\div13}{65\div13} = \frac{3}{5}$

Answer:

$\sin K = \frac{3}{5}$
$\cos J = \frac{3}{5}$