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Tap every function whose domain is [−1, 1]

Exercise and reference answers

Questions
  1. Items
    1. Text
      sin⁻¹ x
      Matches the category
      Yes
    2. Text
      cos⁻¹ x
      Matches the category
      Yes
    3. Text
      tan⁻¹ x
      Matches the category
      No
    4. Text
      sec⁻¹ x
      Matches the category
      No
    5. Text
      cot⁻¹ x
      Matches the category
      No
    6. Text
      cosec⁻¹ x
      Matches the category
      No
    Category
    Domain is [−1, 1]
  2. Items
    1. Text
      tan⁻¹ x
      Matches the category
      Yes
    2. Text
      cot⁻¹ x
      Matches the category
      Yes
    3. Text
      sin⁻¹ x
      Matches the category
      No
    4. Text
      cosec⁻¹ x
      Matches the category
      No
    5. Text
      sec⁻¹ x
      Matches the category
      No
    6. Text
      cos⁻¹ x
      Matches the category
      No
    Category
    Domain is all of R
  3. Items
    1. Text
      cosec⁻¹ x
      Matches the category
      Yes
    2. Text
      sec⁻¹ x
      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
    Domain leaves out the open interval (−1, 1)

Explanation

sin⁻¹ and cos⁻¹ are the two inverses defined exactly on [−1, 1], because sine and cosine themselves only ever output values in that interval. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.
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