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Session 3265

A Geometrical Derivation of the Three Trigonometric Identities

Bertram Pariser

TCI, the College for Technology

Abstract

Hearing the word trigonometry often produces a feeling of hopelessness in adults. Memory banks recall the acronym “SOHCAHTOA” (a factious Indian Word!) which when verbalized stimulates thoughts about the sides of a triangle. After completing a six-month course in trigonometry in high school and graduating from MIT and receiving a Ph.D. from Columbia University, I was convinced that I knew trigonometry cold! However, I now teach physics and mathematics to college students, who frequently do not get it!

Background of Class

This paper is a topic in a mathematics class, MAT201, Mathematical Analysis ll. The textbook used in this course is Caulter, Paul A & Michael A. “Technical Mathematics with Calculus Fourth Edition(1). Students taking this course major in both Electrical Engineering Technology and Computer Science Technology. The course is taken in the second semester. The fall 2002 class consisted of 18 students, 15 male and 3 female. The student ages ranged from 19 to 53. One student is white, six are Hispanic, five students are black, and five are Asian.

Many of our students have deficits in mathematics. They find word problems very difficult. The scientific method starts by formulating a problem. How do you teach students to formulate problems? My approach is to have students construct a triangle and then step by step derive the trigonometric identities. With this hands on approach to mathematics students acquire an understanding of basic concepts rather than relying on rote memorization.

Introduction

Confucius said, “A journey of 1000 miles begins with a single step”

Acquiring an understanding of trigonometry should begin by constructing a right triangle. (Figure 1). Draw a straight line. Place a compass point on the line and mark off two points on opposite sides of the point. Move the compass point to the marked off points and draw an arc on top and an arc on the bottom. Next move the compass to the second marked off point and draw an arc on top and on the bottom. The two arcs intersect above and below the

“Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright © 2003, American Society for Engineering Education”

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Pariser, B. (2003, June), A Geometrical Derivation Of The Three Trigonometric Identities Paper presented at 2003 Annual Conference, Nashville, Tennessee. 10.18260/1-2--11914