9 - Clear Sailing with Trigonometry

Summary

Introduction

Does anyone care about trigonometry? Certainly many of our students don't, aside from the exigency of getting through their exams. As mathematics teachers, we have passion for our subject for its own sake — but we often justify ourselves to our students in terms of what the mathematics can accomplish elsewhere. For trigonometry as for many other topics, this takes the form of the widespread “word problems”: how high is that pine tree across the street? How far did that motorboat travel when it went across the lake? And here we reach a crucial pedagogical problem: few of us really care precisely how tall the tree is, or how far the boat went. We find ourselves forced into producing “baby” problems like these with little real relevance, assuring our students (with fingers crossed behind our backs) that the genuine applications — too complex for their immature minds — hopefully work kind of like these ones do.

Meaningful contexts are surprisingly hard to find. Some pedagogical efforts are searching for realistic classroom friendly projects, and are having some success. However, one source that might easily be overlooked is the history of the subject. Two thousand or more years of human experience is a powerful resource on which to draw. Mathematical subjects arise for good reasons, and bringing these reasons to light can motivate more honestly what otherwise might appear dull, even deceptive in its fake “applications”.