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Match each inverse function to its principal value branch

Exercise and reference answers

Matching pairs
  1. Left
    sin⁻¹ x
    Right
    [−π/2, π/2]
  2. Left
    cos⁻¹ x
    Right
    [0, π]
  3. Left
    cosec⁻¹ x
    Right
    [−π/2, π/2] − {0}
  4. Left
    sec⁻¹ x
    Right
    [0, π] − {π/2}
  5. Left
    tan⁻¹ x
    Right
    (−π/2, π/2)
  6. Left
    cot⁻¹ x
    Right
    (0, π)

Explanation

The principal branch is the one interval on which the function is made one-one so the inverse is single valued. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.
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