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The inverse trigonometric functions arcsin, arccos and arctan reverse the trig functions over a restricted domain. This topic covers their graphs, domains and ranges, and using them to solve equations and find exact angles. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
The inverse functions return the principal value only, within a restricted range. To find every solution, use the symmetry of the original graph. The restricted range exists so the inverse is a genuine function.
Before you start
The groundwork here is trig graphs and domain and range. Pure 3 is where it is assessed. It underpins solving equations and calculus. The topic sits within Trigonometry.
What you learn
arcsin, arccos and arctan undo the trig functions — but only after their domains are restricted. An inverse can only exist if each output comes from exactly one input. An inverse graph is the base graph reflected in the line y=x. Anything inside the bracket acts on the input → it changes the DOMAIN. The course works through why we restrict the domain, how to sketch the three graphs, transformations: outside and inside, finding the domain of a transformed graph and exact values and the composite trap. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Inverse Trig Functions is part of the Trigonometry strand of our free A-level maths courses, studied in the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Related topics students usually take next include R sin(θ + α) Form, Radians, Arcs & Sectors, Reciprocal Trig Functions, Sine & Cosine Rules and Solving Trig Equations. Endless extra practice on this strand is available on the Trigonometry revision engine, which generates a fresh question each time.
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