TestMum
← 2021 HSC Extension 1 paper Question 11(g)

Variation 1 · answer guide

Trigonometric equation — Similar cubic in cos

Question

Solve for by factorising.

This practice question was inspired by Question 11(g) in the 2021 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: rewrite the equation into a familiar trig form, solve each branch, then filter by the interval.Group: .
  2. Simplify the previous line carefully, keeping exact values where possible. or .
  3. Finish the calculation, then check that the result meets the question’s conditions.; ; .
  4. State the final answer clearly in the form the question requested.Solutions: .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Factor structure mirrors the sine cubic.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

← Back to 2021 HSC Extension 1 paper Question 11(g)