The function y = sin(2x) reaches its maximum value when the sine function itself is at its maximum. The sine function achieves its maximum value of 1 at angles of the form:
- θ = π/2 + 2kπ, where k is any integer.
For our function, we need to find when:
- 2x = π/2 + 2kπ
To find the smallest positive value of x, we can set k = 0:
- 2x = π/2
- x = π/4
Thus, the smallest positive value for x where y sin(2x) reaches its maximum is:
- x = π/4 (approximately 0.7854).