When learning trigonometry; I found that the representation of a rotating unit vector was very helpful in visualizing sine and cosine values.
https://en.wikipedia.org/wiki/Trigonometric_functions
https://en.wikipedia.org/wiki/Unit_vector
I came across the Trammel of Archimedes 3D print by Igbu on thingiverse. I was reminded of the fact that sine and cosine values are simply the projection of the unit vector on the x (cosine) and y (sine) axes. This model could be modified to show that relationship.
https://en.wikipedia.org/wiki/Trammel_of_Archimedes
I modified the design in TinkerCad to produce this rough prototype:
You use the bar as a pointer to the angle in question. In the picture above the angle selected is approximately +45 degrees. The Sine value is read from the y axis, the red slider. The Cosine value is read from the x axis, the green slider. The values range from 1 to -1. For the Sine values +1 is at the top (90 degrees) and -1 at the bottom (270 degrees). 0 is in the middle. For Cosine the scale is rather strange, resulting from the counterclockwise rotation. This requires that Cosine values are +1 on the left (180 degrees) and -1 on the right (0 degrees). 0 is in the middle.
Here are some examples:
Place the pointer at 0 degrees and read Sine value (red) at 0 and cosine value (green) at 1.
Place the pointer at 90 degrees and read Sine value (red) at 1 and cosine value (green) at 0.
Place the pointer at 180 degrees and read Sine value (red) at 0 and cosine value (green) at -1.
Place the pointer at 270 degrees and read Sine value (red) at -1 and cosine value (green) at 0.
Angles in between must be interpolated to give approximations of the values.
I have found a number of memory aids for trigonometry, but believe this to be a unique approach. Thanks to lgbu.
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