Question

express the trig ratios as fractions in simplest terms.
answer attempt 1 out of 8
cos k =

sin l =

cos k and sin l .

Explanation:

Step1: Recall cosine definition

For angle $K$, $\cos K = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos K = \frac{JK}{KL} = \frac{39}{65}$

Step2: Simplify the fraction

Divide numerator/denominator by 13: $\frac{39\div13}{65\div13} = \frac{3}{5}$

Step3: Recall sine definition

For angle $L$, $\sin L = \frac{\text{opposite}}{\text{hypotenuse}}$
$\sin L = \frac{JK}{KL} = \frac{39}{65}$

Step4: Simplify the fraction

Divide numerator/denominator by 13: $\frac{39\div13}{65\div13} = \frac{3}{5}$

Step5: Compare the two values

Both $\cos K$ and $\sin L$ equal $\frac{3}{5}$, so they are equal.

Answer:

$\cos K = \frac{39}{65} = \frac{3}{5}$
$\sin L = \frac{39}{65} = \frac{3}{5}$
$\cos K$ and $\sin L$ are equal