Final answer:
The exact solutions to the equation sin(4x) = 0 in the interval [0, 2π) are x = 0, π/4, π/2, 3π/4, ...
Step-by-step explanation:
To solve the equation sin(4x) = 0 in the interval [0, 2π), we need to find the values of x that satisfy the equation.
Since the sine of an angle equals 0 when the angle is 0, π, 2π, etc., we can set the expression inside the sine function equal to these values and solve for x:
4x = 0, π, 2π, 3π, ...
Dividing each of these values by 4, we get:
x = 0, π/4, π/2, 3π/4, ...
These values of x are the exact solutions to the equation sin(4x) = 0 in the given interval.