50% developed


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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.


Wikibook Development Stages
Sparse text 0% Developing text 25% Maturing text 50% Developed text 75% Comprehensive text 100%

Trigonometry Book 1[edit | edit source]

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 Enthusiasts25% developed" 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 Triangles[edit | edit source]

Trig Functions for Triangles[edit | edit source]

Trig Functions as Functions[edit | edit source]

Trigonometry References[edit | edit source]

For Enthusiasts[edit | edit source]

Teachers Notes[edit | edit source]

Trigonometry Book 2[edit | edit source]

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 Geometry[edit | edit source]

More on Trigonometric Identities[edit | edit source]

Going Spherical[edit | edit source]

Applications[edit | edit source]

Circles, Points and Triangles Associated with a Triangle[edit | edit source]

Application to Algebra[edit | edit source]

Surveying[edit | edit source]

Applications to Graphics[edit | edit source]

Where do These Belong?[edit | edit source]

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

for Enthusiasts[edit | edit source]

Teachers Notes[edit | edit source]

Scrap Heap[edit | edit source]

These are pages that are on the way out.

Trigonometry Book 3[edit | edit source]

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 numbers[edit | edit source]

Basis Functions[edit | edit source]

Beyond the Fourier Transform[edit | edit source]

Where do These Belong?[edit | edit source]

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

for Enthusiasts[edit | edit source]

Teachers Notes[edit | edit source]

Authors[edit | edit source]

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.