On the Wonders of the Unit Circle

On the Wonders of the Unit Circle - student project

I wonder how many members of the United States Congress or The New York Times Editorial Board know what the cosine of pi over two is? It's zero. A big fat "Oh". Maybe with a line through it, if you're feeling fancy.

If I had to guess, and I'm going to, I'd say that maybe a third of all those bigwigs who get paid to be smart on behalf of people all across America know that cos(pi/2) = 0. Another quarter might get it in two guesses, and the last half would find a clever way of saying that they don't know, while convincing you that they do know, all while telling you that the taxpayer or subscriber doesn't need to know anyhow. Of course, that doesn't add up to a full complement of New York Times Editorial Board and US Congress members, but rather an additional sixth of individuals, who probably slipped in through the back door on the hope that there would be donuts.

My mother, who doesn't understand that there are numbers less than zero, would say that I deserve a Noble Prize for my scientific method. My father, who had an uncle with a PhD in Geology, would say that a 17% error would be entirely unacceptable, in any experiment. My sister, who think's I'm just another weirdo shut-in, would say "beat it, freak", and slam the door in my face.

Now, you might be wondering how a weirdo shut-in like myself comes to know about such marvelous mathematical wonders as the cosine of pi divided by two. Two words: unit circles.

I like circles. I like them rather a lot. They happen, for some strange reason, to be completely devoyd of sharp corners. This is a rather useful featur, if you happen to not want to poke anything. Another fun feature of circles is that they are round. Mostly, that's the same thing as not having corners, but it sounds different. Circles are great, because it's almost impossible to stack them nicely without them slipping and falling and generally causing mayhem. And watching mayhem insue is one of my favourite past-times. There are other reasons to like circles, if you're a geometry nerd, but I'm not. I just like circles because they can cause people to do stupid things. 

Now, the unit circle is a pretend circle with a radius of "1". It's the most boring circle possible, which is really saying something, because everyone knows that circles are the most boring shape possible, due to their previously noted lack of points. Some might even say that you should never waste time drawing circles, because they're completely pointless. But that's a joke, and unrelated to the unit circle. Now, the fun thing with the unit circle is that it's made by rotating the imaginary radius around the origin, transkribing an arc of theta radians. Radians are a fancy way of measuring angle, kind of like degrees, except with pi. That's why it's such a shame math class comes after lunch, because talking about radians always makes me hungry. Now, cosine and sine are fancy "functions  that take the angle theta and throw out some number instead. If you imagine that the radius forms a triangle with the x-axis of angle theta, cosine is the length of the bottom part of the triangle, along the x-axis, and sine (which is kind of like cosine's messed-up twin brother) is the length of the line that finishes the triangle by connecting the tip of the radius to the x-axis. It's kind of hard to explain without drawing it, but if you drew it out like Mr. Hardigan did, then it would make a lot more sense. unfortunately, I was told that I wasn't allowed to draw illustrations here, so, I guess you'll have to draw it for yourself if it doesn't make sense to you.

Of course, radians are kind of weird and messy, so to say you have a "90 degree" angle, you have to say you have a "pi/2 radians" angle. I told you they used pi a lot. Now, you have to imagine that you have a triangle with the radius pointing at a 90 degree angle, so straight upward, and then imagine what the length along the x-axis of that triangle would be. It would be zero, of course! Because that isn't a triangle, that's a line!

So, in conclusion, radians make me hungry, the unit circle is harder to explain than I thought, and US Congressmen don't know as much about at least one thing as I do. And that's why math is important.

While I'm impressed you managed to stay this coherent despite doing this assignment during your previous class, I'd be more impressed if you had managed to complete the assignment the night before, instead of using Mr. Hardigan's valuable time to complete what you should have already finished. Since the assignment was to write about something you were passionate about, I was glad to hear you have found passion in triginometry, and I expect Mr. Hardigan will be very pleased and confused that you do not have better grades in his class. Your voice was consistent, and you managed to keep the spelling and grammar mistakes to a minimum. 6.5/10.