2022 HSC Mathematics Extension 1
Question 1:
Inverse trigonometric functions
It is given that .
Which of the following is the value of ?
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 . Any angle outside this interval cannot be the value of .
- Option A (), option D (negative) and option B ( has cosine ) are therefore eliminated by range or by the cosine value.
- Note that , and .
- Hence .
- Answer: C. (NESA multiple-choice key: C.)
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
It is given that . What is ?
Question 2
Given , evaluate .
Question 3
Given , the value of is