2023 HSC Mathematics Extension 1
Question 5:
Inverse trigonometric functions
Which of the following is the value of given that ?
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
- The range of is , so equals only when already lies in that interval.
- For , is in the third quadrant relative to the unit circle; is negative.
- The co-terminal principal value in with the same sine is : note and .
- Check: if , then and .
- Option A is positive in this interval (wrong sign for principal sine); C ignores the branch; D is too large in magnitude.
- Answer: B. (NESA multiple-choice key: B.)
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
If , then equals
Question 2
If , then equals
Question 3
If , then equals