Why do we add intervals of 2pi to our solution

The video tutorial explains how to determine all solutions for the equation cosine of X equals sqrt 2 / 2. It covers the use of the unit circle to find specific angles and the graph of cosine to understand periodicity. The tutorial also discusses the concept of adding 2π to find all possible solutions, emphasizing the infinite nature of solutions due to the periodic nature of the cosine function.

Describe the behavior of the cosine graph between 0 and 2π.

How do you find all solutions for cosine of X = sqrt 2 / 2 beyond the interval of 0 to 2π?