Why do we add intervals of pi halves to our solution

The video tutorial explains how to find all solutions for the equation tangent equals ±1. It begins by identifying solutions within the interval 0 to 2π using the unit circle. The instructor then demonstrates how to graph the tangent function to visualize solutions beyond this interval. By understanding the periodic nature of the tangent function, the instructor shows how to extend solutions using π halves increments, avoiding redundancy. The final solution is expressed as X = π/4 + π/2 N, covering all possible solutions.

Explain how the tangent function behaves on the unit circle.

What are the four angles where tangent equals plus or minus one on the interval of 0 to 2π?

Describe the process to find all solutions of tangent equals plus or minus one.

What is the significance of the vertical asymptotes in the graph of the tangent function?

What is the relationship between the solutions of tangent and the unit circle?

How can you express the general solutions for tangent equals ±1 using π?

Discuss the redundancy in writing all solutions for tangent equals ±1.