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← 2023 HSC Extension 1 paper Question 11(e)

Variation 2 · answer guide

Trigonometric equation — Minus sine

Question

Solve for .

This practice question was inspired by Question 11(e) in the 2023 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..
  2. Simplify the previous line carefully, keeping exact values where possible..
  3. Finish the calculation, then check that the result meets the question’s conditions. or (check both in range).
  4. State the final answer clearly in the form the question requested.Verify: at : ; at : .

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

Verification: Auxiliary angle with cosine form.

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

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