Trigonometry-Teaching Aid


Trigonometry-Teaching Aid


     Trigonometry is much easier to learn when the graphical relationships are shown.  Each of the six trig functions is represented in the diagram of an arm sweeping around a circle.  


            This simple circle with its included angle and related parts is the basis for the mechanical device shown which derives, and illustrates the derivation of, the six trigonometric functions of an angle:  


       Shown is a circle 2 units in diameter (ex.: 2 inches in diameter).  As the angle sweeps through the quadrants, the straight lines on the circle, labeled as trig functions, change position (and therefore length) staying always at a length in relationship to the radius of one unit (or 1 inch in this example) which corresponds to its numeral value listed for that trigonometric function at that particular angle.  

       This “trig machine” would best be used as a teaching aid to illustrate the six trigonometric functions of an angle and their relationships to each other.  Accuracy equal to a slide rule should be possible in a small model for student use.  

       The values of the tangent, cotangent, secant, and cosecant range from zero to infinity, however the machine achieves a false infinity marking so that the machine can be made a practical size.  The infinity mark however reads correctly, and it will pose little problem for the student once it has been explained.  

       As the angle indicator crosses the points marked 90, 180, 270, and 360 degrees the quadrant mask should snap from one quadrant to the next, exposing only the quadrant containing the angle pointed to by the indicator. 



Cardboard and thumbtack mockup.


      For more information, please contact Steve Hines at:



Glendale, California, USA