Inverse trigonometric functions — An inverse-cosine graph

Question

Sketch , stating its domain, range and three key points.

This practice question was inspired by Question 14(d) 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: use the restricted domain and range that make the inverse function single-valued. gives .
Simplify the previous line carefully, keeping exact values where possible.The range of is .
Finish the calculation, then check that the result meets the question’s conditions.Evaluate at and join with a decreasing curve.
State the final answer clearly in the form the question requested.Final answer: Domain , range ; points .

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

Verification: Applying cosine to each y-value returns at all three key points.

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