Started trigonometry last week. So far, I actually like it better than algebra. In algebra, the rules change depending on the context of the problem your solving. (My biggest hurdle – Identifying the type of problem, understanding the context/parameters and then recalling all the rules and tools for solving.)
Not to mention that graphically, there is a huge array of possible transformations to the basic functions.
Trig and it’s functions are all based on the circle. (Or the unit circle more specifically) That’s so Zen!
There is an inherent symmetry there…I like that. It makes sense to me. I can quickly solve distances between points based on symmetry. I think it also goes back to my “visual” learning style. Once you have the 4 quadrants, 6 functions and the 3 Pythagorean identities down, The equations are much easier (at least for me) to solve. I have 1 little section I need to work on involving adding and subtracting the distances of pi, but I don’t feel like I’m lost in a forest of tall trees.
Things that are helping-
I’ve been working on memorizing all of the reference and terminal points of the unit circle. Throughout the day when I find myself waiting or killing time for something – I will randomly draw the unit circle and see how fast I can rip out the all of the points. I find a great template/worksheet for this here: http://www.embeddedmath.com/downloads/
flash cards for memorizing the six functions: cosine, sine, secant, co-secant, tangent, cotangent and the 3 Pythagorean identities.
and then flash cards for an array of sample problems all mixed up.
We started graphing the functions this week. (Both by ‘guestimating’ by using transformations and with the calculator)
Before I even saw it, I knew what sine looks like graphically being the audiophile that I am, musician and synth head. The sine wave is a popular building block for creating synth sounds. Nice to correlate my knowledge of audio manipulation to math!
The visual learner in me also loved that my Professor explained that the x-axis is like taking the unit circle, snipping it at zero and pulling it horizontally like a string.
Yes, I’m loving trig…people look at me like I’m psychotic when I say that.
During spring break I’ll be working through my new deck of index cards with random problems and working the hell out of them. [I need an A on the next 2 exams and a C on the final. (But I'll shoot for higher)].
