An even function is one where $f(x) = f(-x)$ for all $x$ in the domain of the function. Let's analyze each option to determine which one represents an even function:

1. $y = \cos(x)$:
   $\cos(-x) = \cos(x)$.
   Therefore, $y = \cos(x)$ is an even function.

2. $y = \sin(x)$:
   $\sin(-x) = -\sin(x)$.
   Therefore, $y = \sin(x)$ is an odd function, not even.

3. $y = \tan(x)$:
   $\tan(-x) = -\tan(x)$.
   Therefore, $y = \tan(x)$ is an odd function, not even.

4. $y = \cot(x)$:
   $\cot(-x) = -\cot(x)$.
   Therefore, $y = \cot(x)$ is an odd function, not even.

Conclusion:

The only even function among the options is $y = \cos(x)$.

Would you like further details or have any questions?

Related Questions:

1. What are the properties of odd functions?
2. Can a function be neither even nor odd? Provide an example.
3. How can symmetry in graphs help identify even or odd functions?
4. What is the significance of periodicity in trigonometric functions like sine and cosine?
5. How would you determine if a more complex function, like $f(x) = x^4 + \cos(x)$, is even?

Tip:

To quickly check if a function is even or odd, substitute $-x$ for $x$ and see if the function remains unchanged (even) or becomes the negative of the original (odd).