Inverse Trigonometric Functions

Topics in this chapter

• Inverse Trig Definitions And Values
• Principal Values, Domains And Ranges
• Inverse Trig Identities And Relations
• Inverse Trig Addition Formulas
• Double-Angle And Half-Angle Formulas
• Inverse Trig Equations And Periodicity

Cheat sheet

Practice questions

1. Question 1Q-3EF52B

   Using the principal value of the inverse sine function, find sin⁻¹(−√3/2).

   1. A.−π/6
   2. B.−π/3
   3. C.π/3
   4. D.2π/3
   See the answer and solution
2. Question 2Q-93768B

   For the function f(x) = cos⁻¹(2x − 1), which of the following gives its domain and range?

   1. A.Domain [0, 1] and range [0, π]
   2. B.Domain [−1, 1] and range [0, π]
   3. C.Domain [0, 1] and range [−π/2, π/2]
   4. D.Domain ℝ and range [0, π]
   See the answer and solution
3. Question 3Q-E1EB59

   Evaluate cos⁻¹(cos(7π/6)) using the principal value of cos⁻¹.

   1. A.π/6
   2. B.5π/6
   3. C.7π/6
   4. D.−5π/6
   See the answer and solution
4. Question 4Q-3BEDE4

   Evaluate sin⁻¹(3/5) + sin⁻¹(4/5), and justify your answer using the principal-value ranges.

   See the answer and solution
5. Question 5Q-71A431

   Using the principal value of the inverse tangent function, find tan⁻¹(−√3).

   1. A.−π/6
   2. B.−π/3
   3. C.π/3
   4. D.2π/3
   See the answer and solution