Unit Vec A Dot B = Cos Theta

cults3d

Math was one of my favorite subjects at school thanks to some truly wonderful teachers who made it enjoyable. However, I always found the way trigonometry was taught rather obtuse. This device can be used with students familiar with basic concepts from geometry and algebra to visualize how cosine values used in trigonometry can be computed using a unit vector dot product. The interesting thing is that when one of the vectors is [1,0], the cosine is simply the x value. A quick YouTube video explains it... http://youtu.be/AQ0t7twdW-M In this example, we have an angle of 60° which is π/3 radians, so the unit vectors are A[0.5, 0.866] and B[1,0]. The dot product formula is Ax * By + Ay * By = Cos ø. However, because By is zero, the result is 0.5. Now if we compute the dot product of another two points that we know are 60° apart, namely A[-0.5, 0.866] and B[0.5, 0.866], we get -0.25 + 0.75 for the x and y values, arriving at the same answer, 0.5. If we turn the dial π/3 radians (or 60°), we see the same value in the cosine plot. See instructions for information on how to print and construct this device...