Trigonometry Functions and Inverses Exam

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which of the following statements is/are TRUE? I. All trigonometric functions have inverse over their respective domains. II. The graph of inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging x and y axes.

Neither I nor II

Both I and II

I only

II only (correct)

Which of the following is the domain of y=sin¯¹x?

0 ≤ x ≤ π

-1 ≤ x ≤ 1 (correct)

|x| ≥ 1

π/2 ≤ x ≤ π/2

What is the range of y=2sin¯¹(2x+2)?

0 ≤ y ≤ π

-1 ≤ y ≤ 1

-π/2 ≤ y ≤ π/2

–π ≤ y ≤ π (correct)

Which of the following is NOT TRUE?

The value of sin(sin⁻¹(3π/5)) is 3π/5 Signup and view all the answers

What is the value of cos(sin⁻¹(1/2))?

√3/2 Signup and view all the answers

Which of the following set of angles is arcsin(-1)?

-π/2 + 2nπ Signup and view all the answers

What is the value of cos [sin⁻¹(3/5) + cos⁻¹(5/13)]?

5√7/ 36 Signup and view all the answers

What is the value of sin(arcsin(1 /2 ) - arccos(1 / 3 ))?

1 - 2√6 / 6 Signup and view all the answers

If cos⁻¹x + sin⁻¹(x / 2) = π / 2, then what is the value of x?

√3 Signup and view all the answers

Which of the following is the range of tan¯¹?

-π / 2, π / 2 Signup and view all the answers

Which of the following corresponds to the principal value branch of sec¯¹?

0, π / 2, π Signup and view all the answers

What is the range of the function y=arctan(2x - 1)?

-π / 2 < y < π / 2 Signup and view all the answers

What is the value of cot(sin⁻¹x)?

√(1 + x²) / x Signup and view all the answers

If θ = arctan(cot(π / 4 )), what is θ?

π / 4 Signup and view all the answers

Which of the following statements is TRUE? I. COS(π / 6) = CSC(π / 3) II. tan(2tan⁻¹(-1))= 0

Neither I nor II Signup and view all the answers

Which of the following has NO value?

arcsin(-2) Signup and view all the answers

What is the exact value of cos(2arctan(√2 / 4))?

24 / 25 Signup and view all the answers

What is the exact value of tan(2sin⁻¹(√3 / 2))?

-√3 Signup and view all the answers

Which of the following is equivalent to sec⁻¹(-√3 / 2)?

cos¯¹ (-√3 / 2) Signup and view all the answers

Study Notes

Trigonometric Examination

The examination covers trigonometric functions and their inverses.
Students must shade the correct answer on answer sheets.
Solutions should be shown on separate scratch paper.
Scratch paper and answer sheets are to be submitted together.
Key concepts include inverse trigonometric functions, their graphs, and domains.
Range of specific trigonometric functions.
Principal values of trigonometric functions.
Application of trigonometric identities and inverses.
Polar coordinates transformations
Cartesian to polar coordinate conversions
Graphs of polar equations.
Solving for missing variables in trigonometric equations and functions.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz assesses your understanding of trigonometric functions and their inverses. Key topics include inverse functions, their graphs, domains, and applications of trigonometric identities. You'll also tackle polar coordinates and their transformations.