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/sci/ - Science & Math

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4216460 No.4216460 [Reply] [Original]

Hey /sci/. I was bored, fiddling about on the internet last night when I started thinking about derivatives and shit. I started wondering about the angle of a slope, and with a little scribbling saw that the angle of the tangent of the function f at x is just arctan(f'(x)). Just because I couldn't find anything via Google about this shit, I was wondering if stuff like this has any real world applications, or if I just came up with something useless while bored. Anyone know?

>> No.4216482

I was just reviewing some calculus and found the slope expressed as the tangent of the angle, and being equal to f'(x). Which means tan(x)=f'(x), and from there you get x=arctan(f'(x))
It seems useful for basic physics

>> No.4216502
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4216502

>>4216460
>>4216482
I don't get what you are talking about.
>tan(x)=f'(x)
is x on the left hand side the angle of the slope of f?
How does this equal x?
I don't see if you're impying you can compute the slop of any function at any point without using calculus.

>> No.4216505

Yeah that's pretty much what a derivative is about, you are taking infinitely small increments dx and dy so the tangent is oppsite side divided my adjacent side which is just dy/dx

Real world applications? It's fucking calculus man, probably the greatest step in all history of mathematics

>> No.4216513

>>4216505
Just because it's using calculus doesn't mean it automatically has real world applications. E.g., I don't imagine that <span class="math">f'(x) + \int f(x) dx[/spoiler] has any application.

>> No.4216525

>>4216513

Integro-differential equations? They model many biology phenomena, Volterra equation is another example.

>> No.4216533

>>4216525
I guess I was wrong. That's what I get for not doing the most minimal amount of research.

In any case, I'm asking if anyone knows a specific instance of a real world application of this, just because I'm honestly curious. The only potential application I can think of would be in diff. eqs., to limit the rate of change of a function.

>> No.4217742

>>4216533
Pretty much all of physics. Here's an example.

http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations

>> No.4217755

>>4216525
>biology
>using anything higher than babby calculus
nope