circular functions

Work your way through all the Insight Journeys here on circular functions and you will never find any of this material difficult again!

An introduction to the circular functions journey: context, motivation, and how to navigate.

Foundational definitions for circular functions and trigonometry.

Systematic approaches to solving trigonometric equations.

Exploring transformations and properties of circular function graphs.

Exploring the reciprocal trigonometric functions.

Discover the compound angle identities through geometric reasoning.

Understanding function transformations systematically.

Understanding differentials and their applications in calculus.

Differentials of reciprocal and inverse circular functions, including sec, cosec, cot, arcsec, arccosec, and arccot.

A completely different way of looking at the differential of sin.

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 all six inverse functions

Inverse circular functions for integral substitutions.

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.