Final answer:
The exact solution for the equation on the interval [0, 2) is x = π.
Step-by-step explanation:
To find the exact solutions for the equation 2 sin(x) = -2 on the interval [0, 2), we can start by isolating sin(x) by dividing both sides by 2: sin(x) = -1.
Next, we can look for angles between 0 and 2 radians where the sine function equals -1. Since the sine function oscillates between -1 and 1 every 2 radians, we can see that the only angle satisfying this condition is x = π.
Therefore, the only exact solution on the interval [0, 2) for the equation 2 sin(x) = -2 is x = π.