How to determine the half angle of tangent when given a triangle

The video tutorial covers the evaluation of the cosecant function, starting with its relation to the unit circle and the need to construct a triangle when the point is not on the circle. It explains how to determine the quadrant of an angle based on given constraints and introduces the cosecant function as the ratio of the hypotenuse to the opposite side. The tutorial also covers the tangent of a half angle, providing formulas and calculations, and concludes with final calculations and a summary of the lesson.

What is the relationship between the cosecant function and the unit circle?

How do you determine the quadrant in which an angle lies when given the constraints?

Explain how to apply the Pythagorean theorem in the context of this problem.

What is the significance of the values of sine and cosine in this problem?

Describe the process of simplifying the expression involving sine and cosine as shown in the video.