The Trigtractor—A Visual Aid for Teaching Trigonometry

Abstract

The use of the word, function, in connection with the trigonometric ratios, implies related change. It is difficult, by means of a picture, or even by a series of still pictures, to develop in the pupil's mind this idea of functional change relationship. Failure to develop this concept adequately is the basic cause of very much of the difficulties which arise throughout a trigonometry course. To many, “sin A equals opposite side over hypotenuse, or ordinate over distance,” is a verbal memorization without a clear mental picture, and with the idea of functional dependence entirely lacking. To meet this difficulty in his trigonometry classes at the University of California, Dr. Merton Hill uses a large protractor with a movable radius strip carrying a movable ordinate strip at its outer extremity. The visual aid device pictured and described in this article, which for lack of a better term I call a “trigtractor,” is a further development of this protractor idea. It is a real time saver and simplifies matters much in: (1) teaching clear concepts of the trigonometric functions; (2) representing functions as a single line; (3) explaining changes in the functions from positive to negative and vice-versa from quadrant to quadrant; and (4) comparing functions of angles in one quadrant with those in another, especially in expressing functions of obtuse and reflex angles in terms of functions of acute angles.