Variation 1 · answer guide

Trigonometric equation — Frequency two on full period

Question

How many solutions does have for ?

This practice question was inspired by Question 6 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.; at four points in that interval.
Finish the calculation, then check that the result meets the question’s conditions.Hence four solutions for .
Match the result to the choices and state the correct option.Therefore option B is correct.

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

Verification: Solutions: for .

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