Final answer:
The equation sin(x) = 1/2 has an infinite number of solutions because the sine function is periodic with a period of 2π radians. The general solution set is x = π/6 + n2π and x = 5π/6 + n2π for any integer n, reflecting the function's periodicity.
Step-by-step explanation:
The equation sin(x) = 1/2 does indeed have an infinite number of solutions. In the context of trigonometric functions, when a function such as the sine function equals a constant value, there are an infinite number of angles that satisfy this equation due to the periodic nature of sine. The sine function has a period of 2π, which means it repeats its values every 2π radians. To find the general solution for sin(x) = 1/2, we look at the unit circle where the sine function represents the y-coordinate. The known angles for which sin(x) = 1/2 are π/6 (30 degrees) and 5π/6 (150 degrees) in the first revolution (0 to 2π). However, since the sine function is periodic, these solutions repeat every 2π radians. Hence, the complete solution set can be expressed as x = π/6 + n2π and x = 5π/6 + n2π where n is any integer. This demonstrates the periodicity and the infinite number of solutions for this trigonometric equation.