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.

Which angles on the unit circle have a cosine value of sqrt(2)/2 within the interval 0 to 2π?

• π/3 and 5π/3

• π/4 and 7π/4

• π/6 and 11π/6

• π/2 and 3π/2

What is the maximum value reached by the cosine function on its graph?

• 0

• -1

• 1

• 2

How many complete cycles does the cosine function have between 0 and 2π?

• One

• Two

• Three

• Four

Why do we add multiples of 2π to the initial solutions of a cosine equation?

• To find solutions in the first quadrant only

• To account for the negative values

• To simplify the equation

• To represent all possible solutions across multiple cycles

What variable is often used to represent the multiples of 2π added to the initial solutions?

• Z

• Y

• N

• X