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/sci/ - Science & Math

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5834285 No.5834285[DELETED]  [Reply] [Original]

sinhx, coshx, tanhx etc.

These are pretty cool and all but why are they called hyperbolic functions. Only coshx looks like a hyperbola but I don't think it is one and the other two don't look like them at all.

Speaking of which, I'm still not sure what defines a hyperbola. I mean what are the general characteristics of the shape?

>> No.5834304

It's the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant.

>> No.5834318

Are the foci specific points in the hyperbolas? If so how do you determine where they are?

Can anyone answer my first question?

>> No.5834325

>>5834285
plot (cosh(t), sinh(t))
shit bricks

>> No.5834337
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5834337

>>5834325
ooooooh do they make a hyperbola like sin and cos make a circle?

That's fuckin' neat

>> No.5834357

>>5834325
>>5834337
Ok considering this, are there functions that make a parabola when used in a parametric plot?

>> No.5834364

>>5834357
(t,t^2)

>> No.5834366

>>5834364
Oh yeah, that's obvious. Silly me.

>> No.5834367

>>5834357

(t,t^2)

>> No.5834384

>>5834325
damn bro. I've taken Complex Analysis already, and I know enough QM to know that OP is correct in that "QM is deterministic" thread, but I never did that.

>> No.5834387

>>5834384
Oh you'll be able to answer my next question then.

Where do you use hyperbolics in physics? You use so much maths things in it they have to come into it somewhere right?

>> No.5834390

>>5834318
the foci are points that are surrounded by the branches of a hyperbola. the farther they are from the vertices, the more elongated (or eccentric) the curve.

>> No.5834398

>>5834387
The way powerlines naturally rest is in hyperbolic sins

>> No.5834401

>>5834387
Anytime you take Fourier series
Anytime you have e^x and e^-x

>> No.5834403

>>5834318
in the standard form of hyperbolas
(x-h)^2/a^2 - (y-k)^2/b^2 = 1 (h,k) represents the center and |a| is the distance from the vertices to the center, c^2 is the focal disctance where c^2 = a^2 + b^2

>> No.5834406

>>5834398
Isn't a catenary a hyperbolic cos?

How does the proof for the hanging rope work anyway?

>> No.5834408

>>5834401
Yeah but I mean what kind of physical situation would you be modelling if you were to use hyperbolics. Just an example.

>> No.5834410

>>5834408
Oh yeah, apart from a hanging rope.