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Put the reasoning in order: why an inverse needs a restricted domain

Exercise and reference answers

Steps
  1. An inverse exists only if the function is one-one and onto
  2. Over their natural domains the trigonometric functions are neither
  3. So restrict the domain until the function becomes bijective
  4. On that restricted piece a unique inverse now exists
  5. The agreed choice of piece is called the principal value branch

Explanation

syllabus builds the chapter in exactly this order: an inverse needs one-one and onto, trigonometric functions are neither over their natural domains so the domain is restricted until they are, and that choice names the principal branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.
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