To solve the equation $\sin(x) = 0.5$, we need to identify the angles for which the sine value equals $0.5$.

The sine function is periodic, meaning it repeats its values at regular intervals. Specifically, for the sine function, this interval is $360$ degrees (or $2\pi$ radians).

First, let’s recall the unit circle and the key angles with known sine values. The sine of $30$ degrees (or $\frac{\pi}{6}$ radians) is $0.5$, which gives us one solution:

However, since the sine function is positive in both the first and second quadrants, we must also consider another angle in the second quadrant that yields a sine value of $0.5$. This angle can be found by subtracting $30$ degrees from $180$ degrees, yielding:

or in radians,

Given the periodicity of the sine function, these solutions will repeat every $360$ degrees. Therefore, the general solutions can be expressed as:

where $n$ is any integer.

In radians, the solutions can be written as:

where $n$ is any integer.

By leveraging the periodic properties of the sine function and employing the unit circle, we can find all possible solutions to the equation $\sin(x) = 0.5$.