2024 HSC Mathematics Extension 1
Question 4:
Inverse trigonometric functions
What are the domain and range of the function ?
How to recognise this question
Question type: inverse trigonometric functions
- The command and notation point to inverse trigonometric functions.
- The requested response is a multiple choice.
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
- For and one needs . Here , so .
- Use the identity for all .
- Hence constantly on the whole domain.
- Domain is the closed interval ; range is the singleton .
- Answer: A. (NESA multiple-choice key: A.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
What is the range of on its natural domain?
Question 2
Domain of is
Question 3
On its domain, equals