2020 HSC Mathematics Extension 1
Question 11(d):
Trigonometric equation
By expressing in the form , solve for .
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 , so (acute).
- .
- Equation: .
- General: or .
- In : or (discard ).
- NESA: 4 marks complete; 3 for form plus one solution; 2 for finding and ; 1 for finding .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 4 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 and solve for .
Question 2
Express as and solve for .
Question 3
Express as and solve for .