Question

express the trig ratios as fractions in simplest terms.

answer attempt 2 out of 2
$cos x = \frac{4}{5}$
$sin w = \frac{4}{5}$
$cos x$ and $sin w$ are equal because $overline{vx}$ is opposite $angle x$ and adjacent to $angle w$.
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Explanation:

Step1: Recall cosine definition

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Calculate $\cos X$

For $\angle X$, adjacent side = $56$, hypotenuse = $70$.
$\cos X = \frac{56}{70} = \frac{4}{5}$

Step3: Recall sine definition

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step4: Calculate $\sin W$

For $\angle W$, opposite side = $56$, hypotenuse = $70$.
$\sin W = \frac{56}{70} = \frac{4}{5}$

Step5: Correct side-angle relationship

$\overline{VX}$ is opposite $\angle W$ and adjacent to $\angle X$, making $\cos X = \sin W$.

Answer:

$\cos X = \frac{4}{5}$, $\sin W = \frac{4}{5}$; $\cos X$ and $\sin W$ are equal because $\overline{VX}$ is opposite $\angle W$ and adjacent to $\angle X$.