Solve the equation on the interval $[0, 2 π)$ .
$2 \sin 2 x - 1 = 0$

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Final Answer: The solutions to the equation $2 \sin 2 x - 1 = 0$ in the interval $[0, 2 π)$ are $0.2618$ and $1.3090$ .

Steps

Step 1 ：Given the equation $2 \sin 2 x - 1 = 0$ .

Step 2 ：Isolate the trigonometric function: $2 \sin 2 x = 1$ which simplifies to $\sin 2 x = 0.5$ .

Step 3 ：The solutions to $\sin 2 x = 0.5$ in the interval $[0, 2 π)$ are approximately 0.2618 and 1.3090.

Step 4 ：Final Answer: The solutions to the equation $2 \sin 2 x - 1 = 0$ in the interval $[0, 2 π)$ are $0.2618$ and $1.3090$ .