True or false: principal values

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   A principal value must lie inside the principal value branch.

2. Statement is true

   Yes

   Statement

   sin⁻¹(1/√2) = π/4.

3. Statement is true

   Yes

   Statement

   cot⁻¹(−1/√3) = 2π/3.

4. Statement is true

   No

   Statement

   If no branch is stated, you may pick any branch you like.

5. Statement is true

   Yes

   Statement

   When no branch is mentioned, the principal branch is meant.

Explanation