2022 HSC Mathematics Extension 1
Question 11(e):
Trigonometric equation
Express in the form .
How to recognise this question
Question type: advanced trig equations
- The command and notation point to advanced trig equations.
- The requested response is a worked solution.
How to handle it: rewrite the equation into a familiar trig form, solve each branch, then filter by the interval.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Write .
- Match coefficients: and .
- Then . Since and , is in the fourth quadrant: .
- (take ).
- Therefore .
- NESA: 3 marks correct; 2 for correct argument (or equivalent); 1 for correct .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 3 total marks 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
Express as with .
Question 2
Write as .
Question 3
Find such that for some .