Trigonometric equation — Amplitude identity

Question

The common amplitude in all four forms of is

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.

Set up the solution: rewrite the equation into a familiar trig form, solve each branch, then filter by the interval.Standard identity: with .
Finish the calculation, then check that the result meets the question’s conditions.The same appears in the cosine phase forms.
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: Maximum value of is .

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