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← 2021 HSC Extension 1 paper Question 11(g)

Variation 2 · answer guide

Trigonometric equation — Restricted interval

Question

Solve on .

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. has no solution in .
  2. Finish the calculation, then check that the result meets the question’s conditions.: on , sine is non-negative, so only .
  3. 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: On only the two solutions for .

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

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