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2023 HSC Mathematics Extension 1

Question 11(d):
Inverse trigonometric functions

2 marksinverse trigonometric functions

Find .

How to recognise this question

Question type: inverse trigonometric functions

  • The command and notation point to inverse trigonometric functions.
  • The requested response is a worked solution.

How to handle it: use the restricted domain and range that make the inverse function single-valued.

Watch out: Do not select a formula until its domain, interval, sign and units match the question.

Step-by-step answer

  1. Rewrite to match .
  2. .
  3. So .
  4. Let , : .
  5. NESA: 2 marks correct; 1 mark for rewriting the integrand in a suitable form.

Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.

The paper records 2 total marks for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.

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