Question

express the trig ratios as fractions in simplest terms.
answer attempt 1 out of 2
$sin x = \square$
$cos w = \square$
$sin x$ and $cos w$
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Explanation:

Step1: Recall sine definition

For acute $\angle X$, $\sin X = \frac{\text{opposite}}{\text{hypotenuse}}$
$\sin X = \frac{VW}{XW} = \frac{14}{50}$

Step2: Simplify the fraction

Divide numerator/denominator by 2:
$\sin X = \frac{14\div2}{50\div2} = \frac{7}{25}$

Step3: Recall cosine definition

For acute $\angle W$, $\cos W = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos W = \frac{VW}{XW} = \frac{14}{50}$

Step4: Simplify the fraction

Divide numerator/denominator by 2:
$\cos W = \frac{14\div2}{50\div2} = \frac{7}{25}$

Step5: Compare the two values

Both equal $\frac{7}{25}$, so they are equal.

Answer:

$\sin X = \frac{7}{25}$
$\cos W = \frac{7}{25}$
$\sin X$ and $\cos W$ are equal