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← 2024 HSC Extension 1 paper Question 10

Variation 1 · answer guide

Trigonometric equation — Phase pair for sine forms

Question

If as functions for all with the same , a possible relation is

  1. or with consistent range choices
  2. only
  4. always

This practice question was inspired by Question 10 in the 2024 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.Sine equality: either angles are equal mod or supplementary mod .
  2. Finish the calculation, then check that the result meets the question’s conditions.That yields the classical phase relations used in the four-form rewrite.
  3. 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: The original exam asks for a numerical invariant of all four phases together.

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

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