Question

express \\(cos x\\) as a fraction in simplest terms.

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ for an angle $\theta$.
For $\angle X$ in right triangle $XWV$ (right - angled at $W$), the adjacent side to $\angle X$ is $XW$ and the hypotenuse is $XV$.

Step2: Identify side lengths

From the diagram, $XW = 3$ and $XV=5$.

Step3: Apply cosine formula

Using the formula $\cos(X)=\frac{\text{adjacent to }X}{\text{hypotenuse}}=\frac{XW}{XV}$.
Substituting the values $XW = 3$ and $XV = 5$, we get $\cos(X)=\frac{3}{5}$.

Answer:

$\frac{3}{5}$