The given equation is:

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

### Steps to solve:

1. Multiply both sides by 2 to eliminate the fraction:
   \[
   2\sin(x) = \sin(x)
   \]

2. Subtract \(\sin(x)\) from both sides:
   \[
   2\sin(x) - \sin(x) = 0
   \]
   Simplifying the left-hand side:
   \[
   \sin(x) = 0
   \]

3. Now, solve for \(x\). The general solution to \(\sin(x) = 0\) is:
   \[
   x = n\pi \quad \text{where} \quad n \in \mathbb{Z} \quad (\text{any integer}).
   \]

Thus, the solution is:

\[
x = n\pi \quad \text{for} \quad n \in \mathbb{Z}
\]

Would you like more details on how to solve this step by step or about the sine function properties?

Here are 5 related questions to explore:
1. What are the properties of the sine function?
2. How can we solve \(\sin(x) = \frac{1}{2}\)?
3. What is the general solution for \(\sin(x) = 0\)?
4. How do periodic functions like sine behave?
5. How does this solution relate to the unit circle?

**Tip:** When solving trigonometric equations, remember that functions like sine and cosine are periodic, so they can have multiple solutions within different intervals.

Discover how to solve the trigonometric equation sin(x) = sin(x)/2 using basic trigonometry principles. This step-by-step guide explains key concepts such as the sine function's periodicity and provides a general solution for sin(x) = 0. Suitable for high school students in Grades 9-12.

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