Today, you’ll get a post, I’ve been thinking about writing a while ago. I had this thought, this HATE in me for a while. Time to let it all out… Enjoy.
Adjacent & Opposite
Let’s start with the very basics… I guess most of us, who remotely have some understanding of math have heard of the functions sine and cosine. They both describe the relation of the sides of a right triangle depending on the angle. Cosine describes the ratio of the adjacent side (a, adj) to the angle over the hypotenuse (longest side of a right triangle). Sine describes the ratio of the opposite side (b, opp) to the angle over the hypotenuse.
See the two words in this paragraph heading? Makes sense right, to name adjacent first (since it’s ADJACENT!) and then name the opposite. Why the fuck then is there the ‘co’ in cosine and not in sine?! It would make the fuck sense to name cosine first and the sine! And:
IT WOULD MAKE THE FUCK SENSE TO CALL COSINE SINE AND SINE COSINE!
ABC… easy as XY. Right?!
I think one of the very first things a kid learns when they get introduced to functions and how to plot them is the horizontal axis also called the x-axis is for your input value and the vertical axis or y-axis is for the output value respectivle for function value. Now, if you plot the the unit circle into a graph and draw a line from the origin to anyhwere on the circle, you get a right triangle. The adjacent side is on the x-axis and its value can be expressed with cos(alpha), the opposite side can be expressed with sin(alpha).
My point? It’s X then Y, right? Right?! It makes sense alphabetically. It makes sense math-wise, since its input then output!
Plus then minus, right? RIGHT?!!
Now it gets complex…
But just in the mathematical sense, because we’re looking at the complex form of sine and cosine.
You may or may not know that there’s also a complex way of expressing sine and cosine. In fact, very often mathematicans define both these functions in that very way. Here they are:
Which formula do you find more natural? More beautiful? Which one would you list first? Yeah, right?! The one with the fucking plus between e^(iz) and e^(-iz)! You wouldn’t teach a first grader first subtraction then addition!!! In addition (pun intendend), there’s also this ugly looking, very unreal (pun intended) term 2i. 2i. It even looks ugly when I write it. Compare that to 2. See how nice it looks?!
But wait, there’s more!
There’s the very same issue with the trigonometric identities of sin^2(x) and cos^2(x). Why the fuck is the expression with the plus ranked “second”?! Plus (pun intended), cosine is part of all of the three identities.
In Defense…
In fact, one mathemical reason comes to mind why sine could rightfully be sine. It starts at zero, whereas cosine starts at one. If you’re looking at boundary values, sine is definitely you’re prefered function. However, I think my other points still outweigh this single one.
Which asshole was it?
Okay, after hopfully having convinced you that cosine is the better sine, let’s find out which fucking asshole named this functions that way… Gerard of Cremona translated it from Arabic to Latin. However, that’s something I have to get into the next time. My lunch break is already longer, than it should have been.
