We need to determine if the function $f(x) = \sin(x)$ is even, odd, or neither.

AnalysisTrigonometryFunction PropertiesEven FunctionsOdd FunctionsSine Function
2025/5/17

1. Problem Description

We need to determine if the function f(x)=sin(x)f(x) = \sin(x) is even, odd, or neither.

2. Solution Steps

To determine if a function is even or odd, we need to evaluate f(x)f(-x).
An even function satisfies the condition f(x)=f(x)f(-x) = f(x).
An odd function satisfies the condition f(x)=f(x)f(-x) = -f(x).
f(x)=sin(x)f(x) = \sin(x)
f(x)=sin(x)f(-x) = \sin(-x)
Using the trigonometric identity sin(x)=sin(x)\sin(-x) = -\sin(x), we have:
f(x)=sin(x)=f(x)f(-x) = -\sin(x) = -f(x)
Therefore, the function is odd.

3. Final Answer

The function f(x)=sin(x)f(x) = \sin(x) is an odd function.

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