circular functions
A comprehensive journey through trigonometry, from foundational definitions to inverse functions and beyond.
Definitions
Foundational definitions for circular functions and trigonometry.
Graphs
Exploring transformations and properties of circular function graphs.
Compound Angle Formulae
Discover the compound angle identities through geometric reasoning.
More Differentials
Differentials of reciprocal and inverse circular functions, including sec, cosec, cot, arcsec, arccosec, and arccot.
Differentials Extra
A completely different way of looking at the differential of sin.
Inverse Functions — Definitions
Introducing arcsin, arccos, and arctan — careful definitions using graphs, with domains and ranges.
Inverse Functions — Composition
Identities and compositions of inverse circular functions, including sum formulas for arcsin, arccos, and arctan.
Inverse Functions — Integrals via substitution
Inverse circular functions for integral substitutions.
Inverse Functions — Integrals
Integrals of arcsin, arccos, and arctan using geometric area arguments and integration by parts.
Inverse Functions — Extension
Graphs, domains, ranges, and derivatives of arcsec, arccosec, and arccot, together with compositions and identities involving these functions.