Solve $\sin x=\frac{1}{2},0\le x<2\pi$

Step-by-step solution

1. Step 1 · Reference angle
   $$x_{\text{ref}}=\frac{\pi }{6}$$

   sin(π/6) = 1/2 from the exact unit-circle values.

2. Step 2 · Sign of sine
   $$\text{Quadrants I and II}$$

   Sine is positive above the x-axis, so two solutions exist in one turn.

3. Step 3 · Apply symmetry
   $$x=\frac{\pi }{6},\pi -\frac{\pi }{6}=\frac{5\pi }{6}$$

   Both lie inside the stated interval.