It’s been a while since I took trigonometry. But one thing that has always intrigued me, Where exactly in nature is the tangent wave found?
In case you don’t know, the sine and cosine (which are basically exact copies of each other, ± 90°) are just your most basic waves. The seasonal changes in temperature are based on them, and the heart rhythm is vaguely based on it too. But the tangent wave is weird. It is kind of reminiscent of an S, with its topmost and bottom-most limits going into infinity.
Strange indeed. So where exactly do you find it in nature?
There are two related, but different, concepts that you’re conflating here: The functions and the waves. A snapshot of a sine wave at a given moment of time has the same shape as the graph of a sine function, but the sine function also shows up in contexts that aren’t particularly related to waves. There is no such thing as a tangent wave, but the tangent function shows up in most of the same non-wave contexts as sine or cosine do.
Get a laser pointer and shine it directly at the ground. Raise your arm slowly so that the dot is projected in front of you. The distance between you and the dot is the tangent function of the angle of your arm from the vertical.
Well, it would be if you were standing on an infinite flat plane. (and actually, to work properly, you need a laser pointer that projects two dots in diametrically opposite directions).
Noted, this isn’t a wave function, but the tangent function cannot appear in nature, because it has peaks of infinite value.
As a possible value of something that fluctuates so as to be described as a wave, I’m going to say: never.
Note that I did not say infinity doesn’t exist in nature, I said the tangent wave has infinite peaks - and I think that phenomenon - something real that fluctuates between finite and infinite values, isn’t possible in nature.
I’ll bite. It’s sometimes postulated that the universe itself is infinite, which implies other infinities. However, not all scientists believe that and pretty much everybody acknowledges that the finite speed of light prevents us from ever exchanging information with anything over a certain distance, even in an infinite universe, so no processes can ever be infinite in extent or number.
That’s the only infinity in nature that I know of. Every other sort of infinity we speak of is purely a mathematical or metaphorical concept.
So what actual infinities in nature are you referring to?
Maybe this isn’t all that different from Mangetout’s example, but, if you imagine a rotating light (like the kind on top of a police car) shining onto a wall, the position of the light on the wall could be modeled by a tangent function.
Yep, the “spinning light” motif is the most commonly given example of the tangent function. To actually see the function, you could set up a newspaper on rollers that stream the paper past you at a constant rate. Let’s say it goes left to right. Then you’d set up a laser, powerful enough to burn the paper, above that stream that spins around on a wheel. The laser and wheel are oriented so that the beam sweeps across the paper. That is, perpendicular to the paper’s movement.
After you turn the machine on and collect the scorched paper, you’d see a tangent graph burned into the paper. If you have two lasers instead of one, and they’re on opposite sides of the wheel, you’ll see a repeating pattern of tangent graphs. That is, you’d see the actual graph of tan(x) where the domain is (-infinity, +infinity).
