Answer:
We have the equation:
-3 + sin(-3x) = -7/2
Adding 3 to both sides gives:
sin(-3x) = -1/2
The solutions for sin(x) = -1/2 are x = 7π/6 and x = 11π/6 in the interval [0, 2π).
We need to find the solutions for -3x in the interval [0, π).
For x = 7π/18, we get -3x = -7π/6, which is not in the given interval.
For x = 5π/18, we get -3x = -5π/2, which is not in the given interval.
For x = π/18, we get -3x = -π/2, which is in the given interval.
Therefore, the solution to the equation in the given interval is:
-3x = -π/2
x = π/6