Evaluating the composition of inverse functions

The video tutorial explains how to find the cotangent of the arctangent of X. It begins by introducing the concept and then moves on to understanding the arctangent and creating a triangle. The teacher explains the relationship between the sides of the triangle using the Pythagorean theorem. After solving for the unknown sides, the teacher simplifies the problem, concluding that the cotangent is simply 1/X, without needing to find the hypotenuse.

In which quadrants does the tangent function lie when considering the arc tangent of X?

• First and Second

• First and Fourth

• Second and Third

• Third and Fourth

What does the tangent of X represent in terms of a triangle?

• Adjacent over Hypotenuse

• Opposite over Hypotenuse

• Adjacent over Opposite

• Opposite over Adjacent

What is the formula used to find the hypotenuse in a right triangle?

• a^2 + b^2 = c^2

• a^2 = b^2 - c^2

• a^2 - b^2 = c^2

• a^2 = b^2 + c^2

What is the simplified expression for the cotangent of the arc tangent of X?

• X

• 1/X

• X^2

• 1

Why was finding the hypotenuse unnecessary in this problem?

• The cotangent of the arc tangent simplifies directly to 1/X.

• The hypotenuse was already given.

• The problem was about sine, not tangent.

• The triangle was not a right triangle.