2021 HSC Mathematics Extension 1
Question 11(g):
Trigonometric equation
By factorising, or otherwise, 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
- Group: .
- Factor: .
- So or .
- On : .
- .
- .
- Solutions: .
- NESA: 3 marks full; 2 for all three possible values of , or at least two -values; 1 for noting is a factor root or factoring from the first two terms.
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
Solve for by factorising.
Question 2
Solve on .
Question 3
Let . Factor completely over the reals and state the roots.