Question

express the trig ratios as fractions in simplest terms.
answer attempt 1 out of 5
sin m =
cos n =
sin m and cos n

Explanation:

Step1: Recall sine definition for $\sin M$

Sine of an angle in a right triangle is $\frac{\text{opposite side}}{\text{hypotenuse}}$. For $\angle M$, opposite side = $56$, hypotenuse = $70$.
$\sin M = \frac{56}{70}$

Step2: Simplify $\sin M$ fraction

Divide numerator and denominator by 14: $\frac{56\div14}{70\div14} = \frac{4}{5}$

Step3: Recall cosine definition for $\cos N$

Cosine of an angle in a right triangle is $\frac{\text{adjacent side}}{\text{hypotenuse}}$. For $\angle N$, adjacent side = $56$, hypotenuse = $70$.
$\cos N = \frac{56}{70}$

Step4: Simplify $\cos N$ fraction

Divide numerator and denominator by 14: $\frac{56\div14}{70\div14} = \frac{4}{5}$

Answer:

$\sin M = \frac{4}{5}$
$\cos N = \frac{4}{5}$