For how to help with this book, click here.
  • Do add new material and examples and make corrections. It all helps.
  • Decide whether new material is book 1,2 or 3. We want book 1 to be ready to use in K12 education. Book 3, especially the for-enthusiasts parts can progress to post-graduate level - that's fine - as long as it's still recognisably trig.
  • Have a look at About This Book, and even modify that, so we have a planned structure and so that it's easier for people to know where to add new content.

All help is welcome.

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Trigonometry Book 1Edit

Book 1 is pre-calculus trigonometry. We assume the student is relatively new to algebra and do algebra step by step.

Many of the pages have closely related free/YouTube videos at the Khan Academy. This is by design. Many students find the video presentation helpful with learning mathematical material.

As with all three trigonometry books, we have a "for Enthusiasts " section, which is for the student who finds the normal content and pace too slow and too easy, and yet still needs exercises and practice with Book 1 trigonometry.

Lengths, Angles and Areas in TrianglesEdit

Trig Functions for TrianglesEdit

Trig Functions as FunctionsEdit

Trigonometry ReferencesEdit

For EnthusiastsEdit

Teachers NotesEdit

Trigonometry Book 2Edit

Book 2 is also pre-calculus trigonometry. However, the algebra moves at a brisker pace than in Book 1. The topics are not central to understanding trigonometry as it is usually taught in schools, now that a lot of former content has been dropped.

One rule of thumb of the topics in Book 2 is the union of the set of all topics in high-school contest related to trigonometry, applications, and the topics in the classical book Plane and Spherical Trigonometry by Palmer (link), subtracting any thoroughly discussed topics in Book 1, and excluding any topic that requires substantial use of calculus or the concept of limit (which should be done in Book 3).

The topics are useful, for example, for students interested in maths contests. In the enthusiasts section there are topics and exercises that are useful to students who will go on to do work with computer graphics.

Book 2 trigonometry deepens the understanding of the many relationships between triangles and circles. It also shows how to tackle some harder trigonometric function identities.

More GeometryEdit

More on Trigonometric IdentitiesEdit

Going SphericalEdit


Circles, Points and Triangles Associated with a TriangleEdit

Application to AlgebraEdit


Applications to GraphicsEdit

Where do These Belong?Edit

This section is for Book 2 pages where we don't yet know how they should fit in.

for EnthusiastsEdit

Teachers NotesEdit

Scrap HeapEdit

These are pages that are on the way out.

Trigonometry Book 3Edit

Book 3 uses and builds on calculus, complex numbers, matrices. We assume the student is relatively fluent with algebra. We will often combine simple steps to keep proofs/explanations short. Book 1 is a prerequisite, but book 2 isn't.

There are many computing related topics, particularly in the "for Enthusiasts" section.

Calculus and complex numbersEdit

Basis FunctionsEdit

Beyond the Fourier TransformEdit

Where do These Belong?Edit

This section is for Book 3 pages where we don't yet know how they should fit in.

for EnthusiastsEdit

Teachers NotesEdit


Lmov, Alsocal, Robinson0120,
Evil saltine, JEdwards, llg, Programmermatt, Douglas W. Mitchell

Also thanks to the many contributors to mathematical articles on Wikipedia from which some of the content has been lifted.