Answer:
Explanation:
The function f(x) = sin(x) oscillates between -1 and 1 over the interval [0, 2π). It achieves a maximum value of 1 when x is π/2 and 3π/2.
To see why, note that sin(x) is a periodic function with a period of 2π. This means that it repeats itself every 2π units. In the interval [0, 2π), sin(x) starts at 0 and oscillates between -1 and 1. The maximum value of 1 occurs twice in this interval, once at x = π/2 and again at x = 3π/2. These are the values of x for which sin(x) reaches its maximum in the interval [0, 2π).
Therefore, the value of x for which f(x) = sin(x) achieves a maximum on the interval [0, 2π) is π/2 and 3π/2.