The Wrong Trigonometry

Short Description
Despite the large amount of theory necessary to sustain classical trigonometry, students are. constantly given examples from only a handful of basic …

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Content
The Wrong Trigonometry
N J Wildberger
School of Maths UNSW Sydney
Australia 2052
December 14, 2005
1 What’s wrong with trigonometry?
Trigonometry begins with the study of triangles. A triangle has three side lengths, three vertex
angles, and an area. Classical trigonometry studies these seven quantities and the relations between
them. It then applies this understanding to more complicated figures such as quadrilaterals and
other polygons, along with three dimensional boxes, pyramids and wedges. Then it solves numerous
problems in surveying, navigation, engineering, construction, physics, chemistry and other branches
of mathematics.
Surely understanding a triangle cannot be hard. But each year millions of students around the
world are turned off further study in mathematics because of problems learning classical trigonometry.
Somehow the subject is a lot more complicated than you would at first guess. Why is this?
Is it necessarily so? Are there any alternatives?
Let’s describe the subject of classical trigonometry in a bit more detail. In keeping with tradition,
precise definitions will be avoided, because they are invariably too subtle. Even so, you’ll perhaps
agree that classical trigonometry is difficult, and that it’s not surprising that students don’t grasp
the material well.
Then we’ll reveal a subversive secret-…