Why do we add intervals of pi to our solution

The video tutorial explains how to find all solutions for the equation sine of x equals ±1/2. It begins by identifying solutions within the interval [0, 2π] using the unit circle. The tutorial then demonstrates graphing the sine function to visualize these solutions and extends the concept to find all possible solutions by leveraging the periodic nature of the sine function. The instructor highlights the use of adding π to find additional solutions, simplifying the process by avoiding redundancy.

What new insight or understanding did you gain from this video?