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← 2022 HSC Extension 1 paper Question 11(e)

Variation 2 · answer guide

Trigonometric equation — Both positive

Question

Write as .

This practice question was inspired by Question 11(e) in the 2022 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. Finish the calculation, then check that the result meets the question’s conditions., .
  3. State the final answer clearly in the form the question requested.Result: .

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

Verification: First-quadrant when both matched sines of signs are positive for the cos term.

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

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