Name the principal value branch

Exercise and reference answers

Questions

1. Question

   Principal range of sin⁻¹ x

   Choices

   1. [−π/2, π/2]
   2. [0, π]
   3. (−π/2, π/2)

   Correct choice

   [−π/2, π/2]

2. Question

   Principal range of cos⁻¹ x

   Choices

   1. [−π/2, π/2]
   2. [0, π]
   3. (0, π)

   Correct choice

   [0, π]

3. Question

   Principal range of tan⁻¹ x

   Choices

   1. [−π/2, π/2]
   2. (0, π)
   3. (−π/2, π/2)

   Correct choice

   (−π/2, π/2)

4. Question

   Principal range of cot⁻¹ x

   Choices

   1. (0, π)
   2. [0, π]
   3. (−π/2, π/2)

   Correct choice

   (0, π)

5. Question

   Principal range of sec⁻¹ x

   Choices

   1. [−π/2, π/2] − {0}
   2. [0, π] − {π/2}
   3. [0, π]

   Correct choice

   [0, π] − {π/2}

6. Question

   Principal range of cosec⁻¹ x

   Choices

   1. [0, π] − {π/2}
   2. [−π/2, π/2]
   3. [−π/2, π/2] − {0}

   Correct choice

   [−π/2, π/2] − {0}

Explanation