Evaluating the composition of Functions using Right Triangles

The video tutorial explains how to evaluate the cosecant of the arctan of X divided by the square root of 2. It begins by setting up the problem and noting the absence of a point on the unit circle, necessitating the creation of a triangle. The instructor explains how to find the inverse tangent and create a triangle in the appropriate quadrant. Using the Pythagorean theorem, the hypotenuse is calculated. Finally, the cosecant is determined by dividing the hypotenuse by the opposite side, resulting in the expression sqrt(X^2 + 2) / X.

What is the formula for cosecant in terms of hypotenuse and opposite side?

How do you express the final evaluation of the cosecant function in this problem?