How do you solve the equation sin(x) = 0.5?

To solve the equation sin(x) = 0.5, find the angles where the sine value is 0.5.

To solve the equation sin(x) = 0.5, you need to determine the angles whose sine value is 0.5. The sine function is periodic, meaning it repeats its values in regular intervals. For the sine function, this interval is 360 degrees (or 2π radians).

First, recall the unit circle and the key angles where sine values are commonly known. The sine of 30 degrees (or π/6 radians) is 0.5. Therefore, one solution is x = 30 degrees. However, because the sine function is positive in both the first and second quadrants, there is another angle in the second quadrant that also has a sine value of 0.5. This angle is 180 degrees - 30 degrees, which equals 150 degrees (or π - π/6 radians).

Since the sine function is periodic, these solutions repeat every 360 degrees. Therefore, the general solutions can be written as:
x = 30 degrees + 360n degrees and x = 150 degrees + 360n degrees, where n is any integer.

In radians, the solutions are:
x = π/6 + 2πn and x = 5π/6 + 2πn, where n is any integer.

By understanding the periodic nature of the sine function and using the unit circle, you can find all possible solutions to the equation sin(x) = 0.5.