Free OER Textbook · Web and PDF

This is the future home to Uka Kula Kai Math

An interactive open textbook that teaches trigonometry through Pacific voyaging, navigation, star paths, ocean observation, and culturally grounded mathematical reasoning.

About the Textbook

A Trigonometry Book About Voyaging

This textbook is not only a trigonometry book; it is also a book about voyaging. The goal is for students to see trigonometry not as a collection of abstract formulas, but as a way of explaining the world around us.

The chapters show how peoples across the Pacific have navigated the ocean for generations using the very mathematical principles students encounter in trigonometry: angles, distances, circular motion, triangles, vectors, periodic behavior, and relationships between quantities.

Although rooted in Hawaiʻi, the text includes examples from across the Pacific so students from diverse backgrounds can see themselves and their cultures represented in mathematics. The book weaves together mathematical ideas and cultural contexts to make trigonometry more relevant, meaningful, and exciting.

Each chapter introduces core mathematical concepts and pairs them with culturally grounded examples, worked examples, practice problems, and explorations. The book is freely available as both a web version and downloadable PDF so cost is never a barrier to learning.

Why This Approach

Culturally Grounded and Mathematically Rigorous

The book uses voyaging and navigation as meaningful contexts for rigorous trigonometry. Students encounter mathematics as a tool for making sense of direction, distance, motion, position, and patterns in the natural world.

The goal is not to place culture beside mathematics as decoration, but to show how mathematical thinking lives within practices of observation, movement, relationship, and survival across the Pacific.

Possible Uses

Ways to Use the Text

Adopt as a Course Text

Use the PreTeXt book as the primary or supplemental text for trigonometry, precalculus, or early college mathematics.

Assign Selected Sections

Teachers can assign individual chapters, examples, or explorations connected to navigation and mathematical modeling.

Pair with K–12 Lessons

Use the text alongside the Uka to Kula to Kai K–12 curriculum to build continuity across grade levels.

Access the Free Textbook

The web version is best for interactive reading and navigation. The PDF is best for offline reading, printing, and sharing with students.