Find the period of sin(x).

The period of sin(x) is 2π.

The period of a function is the smallest positive value of T for which f(x+T) = f(x) for all x. For sin(x), we have:

sin(x+2π) = sin(x) for all x

This can be shown using the angle addition formula for sine:

sin(x+2π) = sin(x)cos(2π) + cos(x)sin(2π)
= sin(x)(1) + cos(x)(0)
= sin(x)

Therefore, the period of sin(x) is 2π.

Alternatively, we can use the fact that sin(x) is a periodic function with period 2π by definition. This means that sin(x+2π) = sin(x) for all x, and any multiple of 2π will also satisfy this condition. Therefore, the period of sin(x) is 2π.

It is worth noting that the period of sin(x) is the same as the period of cos(x), since sin(x) and cos(x) are related by a phase shift of π/2. This means that cos(x) has a period of 2π as well.