Classify `f: R->R` , defined by `f(x)=sinx` as injection, surjection or bijection.

Explanation

To classify the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = \sin x \) as injection, surjection, or bijection, we will analyze its properties step by step.

### Step 1: Determine if the function is injective (one-to-one)

A function is injective if different inputs map to different outputs. In other words, if \( f(a) = f(b) \) implies that \( a = b \).

- The sine function is periodic with a period of \( 2\pi \). This means that \( \sin(x) = \sin(x + 2k\pi) \) for any integer \( k \).
- For example, \( \sin(0) = 0 \) and \( \sin(2\pi) = 0 \), but \( 0 \neq 2\pi \).
...