Nick's ePortfolio

Trigonometry

Math 1060-008 

Zeph Allen Smith, Fall Semester 2014

       A single project was assigned as this class' signature assignment. It presented the phenomenon of a weight on a spring being pulled down and asked the student to present various mathematical equations to predict and graph the behavior of the weight. A scan of the completed project has been posted below:

Reflection 

It was frustrating in previous classes knowing that certain natural behaviors such as some of those found in physics could not be computed using my previous knowledge. While I could graph strait lines and more advanced things such as parabolas and hyperbolas, this still failed to show the continuing behavior of things such as light waves or sound waves. Now, not only can I read and extrapolate meaning from sine and cosine waves (along with all other trigonometry graphs), I can create them.

               Even though I am now striving to become an Aeronautical Engineer and plan on observing phenomena such as light and sound in future tests, I believe there are more every-day applications to this level of mathematical literacy. Many parts of our lives behave like the weight on the spring, as the two forces of potential and kinetic energy alternate major roles. The mechanical parts of our lives I believe is the most obvious example, as a biker speeding up and down hills results in predictable changes in speed. But the more complex trends of economics or even how brain waves themselves operate can also be depicted and understood to a degree using sine and cosine waves. Surfers enjoy being affected by wavelength, rock concerts get their high from amplitude, and the list goes on. Understanding things like amplitude allows one to understand the intensity of something, the distance at which the weight drops and rises. Period only has meaning when time is quantified and is added to the equation and frequency is useful in answering the question, “How many times does (blank) happen per (blank)?”

I honestly must answer that this project did little to change my viewpoint on how helpful understanding trigonometry can be, yet that is in part due to my other classes, studies and electrical engineering lab class. For, in that class, I literally measured and observed the waves generated from various circuits and experiments. I have been able to observe that trigonometry isn’t just a way to explain nature, it is nature. Rather than an assortment of tools created by mankind to mimic such phenomena, I feel it is nothing more or less than mankind’s interpretation of those phenomena. I mentioned the change in potential or kinetic energy before, but any oscillation, continually repeating movement or sub-particle behavior works in these ways on its own, whether we have represented them into functions or not. I’m just glad that we have. 

Nicholas Burk

November 25, 2014