Annotated Ideal Harmonic Transformer Math Manipulative

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Treat yourself and your classroom to a machine that shows you how Sine and Cosine relate to angles in action. Check out an animation on my blog at http://swampcastle.blogspot.com/2013/11/harmonic-transformer-for-classroom.html where I've also imported and assembled the models into OnShape, giving you the chance to take it for a virtual spin. Don't be surprised when you're impressed by its capabilities. Learn more about Onshape at http://swampcastle.blogspot.com/2015/08/onshape-shapes-up-great.html The model is available at https://cad.onshape.com/documents/5c003295166a40c699e9ca02/w/8ec0747e1c854c81bd8468e9/e/b660adf4fde44b19baf860fa Here's how to use it: Turn the knob to rotate the arm to any angle and read the value on the Sine and Cosine scales. Keep in mind that Sine and Cosine values are given for a circle with a radius of 1, which is also known as a unit circle. To get lengths for a circle with a different radius, multiply the reading from the machine by your desired radius. Sine and cosine are trigonometric functions of an angle defined by using right triangles. In one figure, a right triangle has been drawn on top of the Harmonic Transformer with the angle set to 30 degrees. The hypotenuse is the radius of the circle shown as a green line. The radius is drawn from the arm's pivot center to the center of the knob where the pin is. The blue horizontal line represents the adjacent side of the triangle and the magenta vertical line represents the opposite side. Notice that the blue side is the same length as the reading on the cosine scale and the magenta side is the same length as the reading on the sine scale.