To solve the problem of finding the value of [tex]\( f(2\pi) \)[/tex] given that [tex]\( f(x) = \sin(x) \)[/tex], we will proceed step-by-step:
1. Understanding the problem:
- We are given a function [tex]\( f(x) \)[/tex] which is defined as [tex]\( f(x) = \sin(x) \)[/tex].
- We need to find [tex]\( f(2\pi) \)[/tex], which translates to finding the value of [tex]\( \sin(2\pi) \)[/tex].
2. Applying the definition of the sine function:
- The sine function is periodic with a period of [tex]\( 2\pi \)[/tex]. This means that [tex]\( \sin(2\pi) \)[/tex] will have the same value as [tex]\( \sin(0) \)[/tex].
- We know from the properties of the sine function that [tex]\(\sin(0) = 0\)[/tex].
3. Conclusion:
- Therefore, [tex]\( f(2\pi) = \sin(2\pi) \)[/tex] is equal to [tex]\( \sin(0) \)[/tex], which is [tex]\( 0 \)[/tex].
So, the value of [tex]\( f(2\pi) \)[/tex] is [tex]\( 0 \)[/tex].
