In today's class, we'll be exploring the following principles: First, the Pythagorean theorem. Second, the reciprocal relationship between sine and cosine. And third, logarithmic functions and how they relate to me not having a damn clue what I've just said.
Now, if you'll take out a sheet of graph paper, I'll show you exactly how screwed I am.
Let us begin by plotting the x- and y-axis. What we have here is what is known as the Cartesian plane or, as you'll soon refer to it, The Moment I Realized Mr. Weinback Was A Complete And Utter Fraud. The parabolic curve I've haphazardly thrown up on the board, this is a mathematical constant, and it gives me a few extra seconds of stalling before I need to panic. Please also note the points I've tried graphing along our curve. These represent the fact that I probably shouldn't be teaching this course.
Everyone with me so far? Good. Me neither.
It's important to remember that, in its simplest form, mathematics is all about identifying properties that are known, and properties that are unknown. Take the equation, a2 + b2 = I'm going to be out of a job very soon. Okay, what do we know? Well, we know that I am clearly in way, way over my head, and we also know that I'm currently saying whatever happens to enter into my brain at this very moment.
Write that down.
Now, what if I were to tell you that the variable a is the rate at which I'm sweating straight through my tweed jacket, and that the variable b is absolute zero or, in other words, my chances of recovering at this point? Can anyone solve this equation now? Can anyone tell me what I'm doing here? Why I shouldn't just pack up my things and leave? Anyone? Anyone at all?
Okay. Perhaps we've gotten a little ahead of ourselves. Why don't we begin instead with the very basics. Trigonometry is the study of triangles. Triangles, as we all know, have three sides. My name is Donald Alan Weinback. I have completely lost both your trust and respect. And this is a classroom. Good. Very good. Let's continue. Three-dimensional objects such as cubes are math-related, so we'll draw several of them up on the board to fill some of this paralyzing white space. Also, there's this thing called a radius, which will be mentioned every time a minute or so passes without me saying a single word. And, of course, you need to know about tangents….
Speaking of tangents, anybody hear about that new Mexican place that opened up down the street? Apparently, they have good burritos. I've always been more of a fajita guy myself, but I'll probably check it out nonetheless. Maybe Thursday, or on Friday. All right then, moving on.
Everyone take out your graphing calculators. Please tell me you all have that Nibbles game on there and can amuse yourselves for 10 to 15 minutes while I sit here and try desperately to collect my bearings. Actually, why don't you take out your compasses and protractors, too. Use them to draw a unit circle. Now find the slope of that circle, if that is in fact a real term and not something I just made up. Furthermore—and this is the most important thing you can take from class today—please do not tell your parents about any of this.
Oh, infinity! Did I mention infinity? You should definitely know something about infinity.
In fact, here's some other math stuff I think I overheard once: pi = r(d2), 3x + 4y = 22x – 8y, a square is always a rectangle but a rectangle is not always a square, and the number 17. Do with these what you will.
Well, I suppose this is as good a time as ever to review what we've covered so far today. First, trigonometry is a field of mathematics, along with geometry and that other field with the fractions. Second, I have absolutely no hope of getting tenure now, I'm profoundly sorry for having wasted the last 50 minutes of your lives, why oh why didn't I go to grad school, and Pythagoras is an important mathematical figure. Please remember all of this information for your final teacher evaluation.
Next week, we'll be taking an exciting dive into the world of differential calculus. I will not be here for that.