https://file.aiquickdraw.com/mathbot/file/1727088898001h37m49gw.jpg

找出偶函数 奇函数 非偶非奇函数

From the image, it looks like the function given is:

\[
y = \sin(\cos(x))
\]

To determine whether this function is even, odd, or neither, we need to apply the following criteria:

- A function \( f(x) \) is **even** if \( f(-x) = f(x) \).
- A function \( f(x) \) is **odd** if \( f(-x) = -f(x) \).

### Step 1: Test for Evenness

Substitute \( -x \) into the function:

\[
f(-x) = \sin(\cos(-x))
\]

Since \( \cos(-x) = \cos(x) \) (the cosine function is even), we get:

\[
f(-x) = \sin(\cos(x)) = f(x)
\]

Thus, \( f(-x) = f(x) \), which means the function \( y = \sin(\cos(x)) \) is **even**.

### Conclusion:
The function \( y = \sin(\cos(x)) \) is an **even function**.

---

Do you need any further details or explanations? Here are some related questions you might find interesting:

1. What is the difference between even and odd functions?
2. Can a function be both even and odd?
3. How does the periodicity of trigonometric functions affect their even/odd nature?
4. What are other examples of even functions besides \( \cos(x) \)?
5. Can you have a function that is neither even nor odd?

**Tip:** When determining whether a function is even or odd, always substitute \( -x \) and simplify to see how the function behaves!

Learn how to determine whether the trigonometric function y = sin(cos(x)) is even, odd, or neither. This problem covers key concepts related to the behavior of even and odd functions, with step-by-step calculations showing how to substitute -x and simplify.

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