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← 2025 HSC Extension 1 paper Question 5

Variation 3 · answer guide

Trigonometric equation — A shifted sine equation

Question

Express as a single sine and solve for .

  1. only
  2. only
  3. or
  4. or

This practice question was inspired by Question 5 in the 2025 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. Simplify the previous line carefully, keeping exact values where possible.Solve both sine branches and filter the interval.
  4. Finish the calculation, then check that the result meets the question’s conditions.
  5. Match the result to the choices and state the correct option.Therefore option C is correct: or

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

Verification: Direct substitution gives at both values.

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

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