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This IB Maths AI AHL Topic 3.9 – Reciprocal Trigonometric Identities resource develops students’ understanding of reciprocal and inverse trigonometric functions. It begins by defining sec(θ), cosec(θ), and cot(θ) as the reciprocals of cos(θ), sin(θ), and tan(θ). Students then explore the graphs of these functions, including their periods, domains, ranges, and vertical asymptotes, before applying the reciprocal relationships to calculate exact trigonometric values.

The lesson also derives and applies the reciprocal Pythagorean identities, including 1 + cot²(θ) = cosec²(θ) and 1 + tan²(θ) = sec²(θ). Students learn how to select an appropriate identity, determine missing trigonometric ratios, and prove identities by rewriting expressions in terms of sin(θ) and cos(θ). The resource then introduces arcsin(x), arccos(x), and arctan(x), with careful attention given to their restricted domains, principal-value ranges, graphs, and important points. With clear definitions, graph summaries, identity derivations, worked examples, proof practice, common-error warnings, and fully worked solutions, this resource helps AHL students build strong trigonometric fluency in line with IB Mathematics AI expectations.