Given Sine, evaluate the half angle of cosine

The video tutorial explains how to find the exact values of cosine using the half angle formulas. It begins by setting up the problem with a given sine value and constraints. The instructor then uses the Pythagorean theorem to find the cosine value, considering the angle's position in the second quadrant. The half angle formula for cosine is applied, and the expression is simplified by rationalizing the denominator, resulting in the final solution.

Describe the process of simplifying the expression after applying the half angle formula.

What steps are involved in rationalizing the denominator in the final answer?