Evaluating the composition of Functions using Right Triangles

The video tutorial explains how to evaluate the cosecant of an arctangent using right triangles. It begins by examining the innermost function, arctangent, and discusses creating right triangles with given values. The tutorial explores different triangle configurations and their positions on the unit circle, emphasizing the importance of the correct quadrant. The Pythagorean theorem is applied to find the hypotenuse, and the final calculation of cosecant is performed using the hypotenuse and opposite side.

What is the innermost function that needs to be evaluated in the given problem?

• Sine

• Cosine

• Arctangent

• Cosecant

Which two quadrants are considered for the angle in the problem?

• First and Fourth

• Third and Fourth

• Second and Third

• First and Second

What is the range of the arctangent function?

• -π to π

• -π/2 to π/2

• 0 to π

• 0 to 2π

What is the hypotenuse of the triangle when using the Pythagorean theorem?

• 5

• 12

• 17

• 13

How is the cosecant of an angle calculated?

• Opposite over Hypotenuse

• Adjacent over Hypotenuse

• Hypotenuse over Adjacent

• Hypotenuse over Opposite