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 first step in evaluating the cosecant of arctan of X divided by sqrt 2?

• Directly calculate the cosecant

• Find a point on the unit circle

• Create a triangle

• Use the sine function

Which quadrants are relevant when dealing with the arctangent function?

• First and second

• Second and third

• First and fourth

• Third and fourth

How do you calculate the hypotenuse in the given problem?

• Using the sine function

• Using the cosine function

• Using the Pythagorean theorem

• Using the tangent function

What is the formula for cosecant in terms of a triangle?

• Hypotenuse over adjacent

• Hypotenuse over opposite

• Adjacent over hypotenuse

• Opposite over hypotenuse

What is the final expression for the cosecant of arctan of X divided by sqrt 2?

• sqrt(2) / X

• X / sqrt(X^2 + 2)

• sqrt(X^2 + 2) / X

• X^2 + 2 / X