To solve the equation sin^2x = 1/2, we can take the square root of both sides:

√(sin^2x) = √(1/2)

This simplifies to:

sinx = ±√(1/2)

Now, we need to find the values of x that satisfy this equation. The sine function has a period of 2π, so we can find the solutions within one period (0 to 2π) and then add 2π to find the solutions in the next period.

Using a calculator or reference table, we find that sin(π/4) = √(2)/2 and sin(3π/4) = √(2)/2.

Therefore, the solutions for x within one period are:

x = π/4 + 2πn, where n is an integer
x = 3π/4 + 2πn, where n is an integer

These solutions cover the range from 0 to 2π. To find the solutions in the next period, we add 2π to each of these solutions:

x = π/4 + 2πn + 2π, where n is an integer
x = 3π/4 + 2πn + 2π, where n is an integer

These are the complete solutions to the equation sin^2x = 1/2.