Inverse Trigonometric Functions

A ramp rises 1 metre along a slope of 2 metres. The sine of its angle is one half. But which angle? Thirty degrees, one hundred and fifty degrees and many more all have the sine one half. To make the question have one answer, mathematicians cut each trigonometric graph to a piece that takes every value once. In this chapter you learn the cuts and the graphs they give, the identities that connect the inverse functions, and how to simplify tangled expressions and solve equations with an angle hidden inside. It covers the unit of the Indian syllabus (NCERT, JEE Main) and the matching topics of A-Level, IB and AP. Python draws every graph and checks every identity.

Part of Mathematics · High School (11–12) (chapter 18)

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Inverse Trigonometric Functions: Domains, Ranges and Graphs

Why can the sine not be undone until we cut its graph? Learn the cuts, called principal value branches, for the six inverse functions. Read their domains, ranges and graphs, and work out values such as

\sin^{-1}(\sin 4)

where the angle lies outside the cut. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topics of A-Level, IB and AP.

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