I have been teaching PreCalculus for the past ten years, and it always bothered me how trigonometry is developed and presented in most books. After having spent months on linear, quadratic, polynomial, rational, exponential and logarithmic functions where we define all of these functions having domains in terms of subsets of the real number set, we now define sine & cosine as having a domain that is a unit for measuring angular rotation. Wouldn't that be like beginning logarithms by saying it is a function that takes in sound intensities and its domain is in terms of watts per meter squared?
It just strikes me as odd. The last few years I have been developing the trig functions by first introducing periodic functions and then the wrapping function. By using the analogy of wrapping a number line around the unit circle, I can develop all six trigonometric functions, their graphs, the basic values for pi/6’s, pi/4’s, pi/3’s, pi/2’s, and many of the basic trigonometric identities all without memorizing. I find it to be a very powerful analogy. I usually do not even discuss degrees & radians until I move onto applications of trigonometric functions later on.
Do any of you use the wrapping function, or do you begin teaching trig using degrees & radians?