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← 2020 HSC Extension 1 paper Question 11(d)

Variation 1 · answer guide

Trigonometric equation — Shift by π/6

Question

Express as and solve for .

This practice question was inspired by Question 11(d) in the 2020 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 (plus as needed).
  4. State the final answer clearly in the form the question requested.In range: or .

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

Verification: Substitute both solutions into the original left-hand side to get .

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

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