Variation 3 · answer guide

Inverse trigonometric functions — Outer factor on constant

Question

On its domain, equals

This practice question was inspired by Question 4 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: use the restricted domain and range that make the inverse function single-valued.Inner sum is for .
Finish the calculation, then check that the result meets the question’s conditions.Multiply by : .
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: Domain is ; value never leaves .

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