Variation 2 · answer guide

Inverse trigonometric functions — Arccos of a negative special value

Question

Given , evaluate .

This practice question was inspired by Question 1 in the 2022 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. returns a value in .
Simplify the previous line carefully, keeping exact values where possible. and is in range.
Finish the calculation, then check that the result meets the question’s conditions. has cosine .
Match the result to the choices and state the correct option.Therefore option C is correct.

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

Verification: Positive cosine maps to an acute principal angle.

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