Inverse Trigonometric Functions
Study inverse sine, cosine and tangent functions, their restrictions, exact values, graphs and calculus links.
Active lessons
5
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
Diagnostic
Take the topic test
A timed, ~60-minute test drawn at random across all 4 subtopics of this unit. You get a marked result, a predicted band, and a clear list of which subtopics to re-practise.
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
5 of 5 active
Lesson 1
Inverse Sine and Cosine
Understand restricted domains, principal ranges, exact values and graph features for arcsin and arccos.
Lesson 2
Inverse Tangent
Use arctan's domain, range, asymptotes and exact values to solve inverse tangent and triangle problems.
Lesson 3
Differentiating Inverse Trig Functions
Differentiate inverse trigonometric functions, apply the chain rule and recognise basic inverse-trig integrals.
Lesson 4
Inverse Trig Identities and Composite Expressions
Prove sin⁻¹(x) + cos⁻¹(x) = π/2, apply it to find unknown inverse trig values, and evaluate composite expressions such as sin(cos⁻¹(x)) using the Pythagorean identity.
Lesson 5
Prior Knowledge Revision: Inverse Trig
Activate prior knowledge for inverse trigonometric functions: exact trig values at standard angles, the ASTC quadrant sign rule, and the compound angle and double angle identities.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.