circular functions

A comprehensive journey through trigonometry, from foundational definitions to inverse functions and beyond.

Foundational definitions for circular functions and trigonometry.

Systematic approaches to solving trigonometric equations.

Exploring transformations and properties of circular function graphs.

Building fluency with fundamental trigonometric relationships.

Exploring the reciprocal trigonometric functions.

Discover the compound angle identities through geometric reasoning.

Understanding function transformations systematically.

Understanding differentials and their applications in calculus.

Developing insight into integration methods and strategies.

Introducing arcsin, arccos, and arctan — careful definitions using graphs, with domains and ranges.

Identities and compositions of inverse circular functions, including sum formulas for arcsin, arccos, and arctan.

Derivatives of arcsin, arccos, and arctan, with applications to integration.

Integrals of arcsin, arccos, and arctan using geometric area arguments and integration by parts.

Graphs, domains, ranges, and derivatives of arcsec, arccosec, and arccot, together with compositions and identities involving these functions.