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← 2023 HSC Extension 1 paper Question 11(e)

Variation 3 · answer guide

Trigonometric equation — t-method only

Question

Using , 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. 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.Corresponding and give and .

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

Verification: Standard solutions of .

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

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