Using composition of inverses using triangles

The video tutorial explains how to evaluate the inverse of tan(X/sqrt2) by constructing a triangle and calculating the hypotenuse to find the cosecant. The process involves understanding tangent as opposite over adjacent, calculating the hypotenuse using the Pythagorean theorem, and deriving the cosecant as the reciprocal of sine. The tutorial concludes with the final answer and a brief closing remark.

What is the first step in solving the problem of evaluating the inverse of tan(X/sqrt(2))?

• Directly calculate the cosecant

• Use the sine function

• Create a new triangle

• Find X on the unit circle

What does the tangent function represent in a right triangle?

• Opposite over adjacent

• Opposite over hypotenuse

• Hypotenuse over opposite

• Adjacent over hypotenuse

Which theorem is used to find the hypotenuse of the triangle?

• Sine rule

• Cosine rule

• Pythagorean theorem

• Tangent rule

What is the relationship between cosecant and sine?

• Cosecant is the same as sine

• Cosecant is the reciprocal of sine

• Cosecant is the reciprocal of tangent

• Cosecant is the reciprocal of cosine

How is the final answer for the cosecant expressed?

• X / sqrt(X^2 + 2)

• sqrt(X^2 + 2) / X

• X / (X^2 + 2)

• X^2 + 2 / X