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Tap every function whose principal range has a point removed

Exercise and reference answers

Questions
  1. Items
    1. Text
      cosec⁻¹ x removes 0
      Matches the category
      Yes
    2. Text
      sec⁻¹ x removes π/2
      Matches the category
      Yes
    3. Text
      sin⁻¹ x
      Matches the category
      No
    4. Text
      cos⁻¹ x
      Matches the category
      No
    5. Text
      tan⁻¹ x
      Matches the category
      No
    6. Text
      cot⁻¹ x
      Matches the category
      No
    Category
    Principal range has a point cut out
  2. Items
    1. Text
      tan⁻¹ x (−π/2, π/2)
      Matches the category
      Yes
    2. Text
      cot⁻¹ x (0, π)
      Matches the category
      Yes
    3. Text
      sin⁻¹ x [−π/2, π/2]
      Matches the category
      No
    4. Text
      cos⁻¹ x [0, π]
      Matches the category
      No
    Category
    Principal range is an OPEN interval

Explanation

cosec⁻¹ drops 0 and sec⁻¹ drops π/2, because cosec and sec are undefined there. The other four ranges are unbroken. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.
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