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We are tasked with solving the trigonometric equation:

\[
\sin(x) = \frac{1}{2}
\]

### Step-by-Step Solution:

1. **Find General Solutions:**
   The sine of an angle is \( \frac{1}{2} \) at specific angles. Using the unit circle, we know that:

   \[
   \sin\left(\frac{\pi}{6}\right) = \frac{1}{2}
   \]

   Additionally, since sine is positive in both the first and second quadrants, the other angle that gives \( \sin(x) = \frac{1}{2} \) is:

   \[
   x = \pi - \frac{\pi}{6} = \frac{5\pi}{6}
   \]

   Therefore, the general solutions to the equation \( \sin(x) = \frac{1}{2} \) are:

   \[
   x = \frac{\pi}{6} + 2k\pi \quad \text{or} \quad x = \frac{5\pi}{6} + 2k\pi
   \]

   where \( k \) is any integer.

2. **Interval [0, 2π]:**
   Now, we need to express the solutions in the interval \( [0, 2\pi] \). In this interval, the two valid solutions are:

   \[
   x = \frac{\pi}{6} \quad \text{and} \quad x = \frac{5\pi}{6}
   \]

### Now, addressing the answer choices:

- **Option A:** This suggests there is only one solution. This is incorrect because there are two solutions in \( [0, 2\pi] \).

- **Option B:** This option suggests there are multiple solutions, and this is the correct one. The two solutions in \( [0, 2\pi] \) are \( \frac{\pi}{6} \) and \( \frac{5\pi}{6} \).

- **Option C:** There are clearly solutions, so this option is also incorrect.

### Final Answer: 
The correct choice is **B**, and the two solutions are \( x = \frac{\pi}{6}, \frac{5\pi}{6} \).

Would you like further details on this? Here are some related questions:

1. How do you find general solutions for sine equations in radians?
2. What is the unit circle and how does it help solve trigonometric equations?
3. Why does the sine function give two solutions in the interval \( [0, 2\pi] \)?
4. What are the key differences between radians and degrees in trigonometry?
5. How do you verify trigonometric solutions using a calculator?

**Tip:** Always remember to consider both quadrants when solving trigonometric equations. For sine, it is positive in the first and second quadrants.

Solve sin(x) = 1/2, finding all solutions. Express the solutions in both radians and degrees.

Learn how to solve the trigonometric equation sin(x) = 1/2 using general solutions and the unit circle. Explore the key solutions in both radians and degrees, with steps to find answers in the interval [0, 2π]. Ideal for students in Grades 10-12.

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