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← 2021 HSC Extension 1 paper Question 7

Variation 2 · answer guide

Trigonometric equation — Negative sine coefficient only

Question

For , which is true?

  1. and
  2. and
  3. and
  4. and

This practice question was inspired by Question 7 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. and so .
  2. Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Matches the original sign pattern with concrete coefficients.

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

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