Inverse & Reciprocal Trigonometric Functions (College Board AP® Precalculus): Exam Questions

Find the exact value of each of the following.

(i)

(ii)

(iii)

Rewrite the expression as an expression in which appears exactly once and no other trigonometric functions are involved.

The function is given by .

Determine the exact value of . Show the work that leads to your answer.

The function is given by .

Determine the domain and the range of . Give a mathematical rationale for both based on the domain and range of the parent function .

The function is given by .

(i) State the range of .

(ii) Determine whether the point is a local minimum or a local maximum of . Give a reason for your answer based on the behavior of the cosine function.

An angle in standard position satisfies , and .

(i) Find the exact value of . Show the work that leads to your answer.

(ii) Find the exact value of . Show the work that leads to your answer.

(iii) Find the exact value of .

The function is given by .

Find the value of , expressed as a decimal approximation. Show the work that leads to your answer.

Find the limiting value of as . Give an exact answer. Show the work that leads to your answer.

Rewrite the expression as a single constant.

The function is given by .

State a restricted domain for on which the inverse function of can be defined. Give a reason for your answer.

The function is given by .

Find all vertical asymptotes of the graph of on the interval . Give a reason for your answer.

Rewrite as an expression in that does not involve any trigonometric or inverse trigonometric functions.

Rewrite the expression as a single term involving .