Variation 2 · answer guide

Trigonometric equation — A quadratic in sine

Question

Solve for .

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.

Set up the solution: rewrite the equation into a familiar trig form, solve each branch, then filter by the interval.
Simplify the previous line carefully, keeping exact values where possible.
Simplify the previous line carefully, keeping exact values where possible. or
Finish the calculation, then check that the result meets the question’s conditions.List the three interval solutions.
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: Each listed angle satisfies .

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