Mathematica Q&A: Plotting Trig Functions in Degrees

[Kathy_Bautista]

If you want to plot trigonometric functions in degrees instead of radians, check out this helpful post in the Wolfram Blog:
http://blog.wolfram.com/2011/03/31/math ... n-degrees/

You can even download the post as a notebook, to help get you started.

Enjoy!

-Kathy

[Andrew_Bayliss]

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?

[Andrew_Bayliss]

Update:

Here is a link to a notebook that contains demonstrations showing the Wrapping Function Identities. It's fairly easy to prove the magnitudes of the coordinates are equal. This is just an example of why I find the wrapping function powerful. If students can draw the relationships based on a small arc length in the first quadrant, then they know all those relationships for all their trig functions. All it is is drawing equal arc lengths off of each quadrantal and adjusting the horizontal & vertical coordinates appropriately.

[Andy_Dorsett]

Andrew -

I feel the same way. When I taught Pre-Calculus, I made sure to emphasize that trigonometric functions were, more than any other functions they saw before, patterns. (I.e. Periodic functions). My students struggled through the wrapping functions idea, but it was always important enough to me to show them this. They were so used to the Adjacent, Opposite, and Hypotenuse definitions from Geometry that it was hard to keep this separate in their minds, at least at first.

With Trig, the memorization seems insurmountable for students. Perhaps if I had stretched the idea of the wrapping function further, the memorization would have been less cumbersome and daunting. And, if memory serves me correctly, wrapping functions in much earlier texts (1960s, 1970s, etc.) held a much larger place than they do now.

Having Mathematica to demonstrate and actual number line wrapping around an actual circle would've made all the difference to my students when I taught.

[Andrew_Bayliss]

There's a great demonstration of this on the Demonstrations Project website. You can wrap a number line labeled with integers or units of Pi/2. You can wrap positively or negatively. It is really nice, and I have used it in class.

Here is the link: http://demonstrations.wolfram.com/WrappingTheNumberLineAroundTheUnitCircle/