Trigonometry
teaching tools developed by Steve Hines during the second year of college.
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Aware of the rote approach used to teach trigonometry, Steve created a series of devices to intuitively illustrate the changing relationships of the six trig functions. The simplest of these devices was a 3 x 5 inch flip movie. |
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...Once a student sees a few basic principles below, even without a calculator, the value of any trig function can be known within 1-2 decimal places. This allows someone to know, for example when a 30° angle is increased, if the tangent increase or decrease? (it increases)
...A few other useful relationships:
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...The first working model was constructed of cardboard, so that a graduated cross translated in a circular motion. When the cross was covered by a mask with a circular opening, and another quadrant mask with one quadrant exposed, the scale directly indicates the sine of the angle (on the vertical scale), and the cosine (on the horizontal scale). The device, in both photos, is set to 45°, and values for the sine and cosine are both slightly over 0.7 (actually 0.707). The purpose of the quadrant mask is to provide horizontal and vertical reference edges, against which the sine and cosine can be read.
...Another slightly more finished device built of wood, Masonite and plastic gears showed the sine and cosine of any angle from 0-360° through a quadrant opening. The device was manually operated, and the quadrant mask had to be rotated to reveal only the quadrant of the angle of interest. The markings for the sine and cosine were marked on the vertical and horizontal members, res., of a simple cross shape which translated around in a circular motion as the angle was adjusted.
....This product is not for sale. Do not contact us to purchase this product. This project is shown only as an example of inventions HinesLab currently offers to clients, as well as a variety of licensable technology.
