Cosine is the derivative of sine.
y = sin(x) - Domain: D = ℝ, x, x0, x<> x0 in ℝ, Δx = x − x0, Δy = f(x)-f(x0).
[sin(x)] ’ = f’(x) = lim (Δy/Δx) = lim [f(x0+Δx)-f(x0)]/Δx = cos(x)
The derivative of sine, y = sin(x) —by its conceptual definition as “slope of the tangent line”— is change-in-y-over-change-in-x = dy/dx = -sin(x)/1 = -sin(x)
Likewise, the derivative of sine is = cos.
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sin = time.
Lay back, have a cigar!
It looks as if the “thumblr”-bug has been repaired, let’s give it a try!
"Hey, swamp! Hey swampy!"
“Yes, Martha? Can I get you something?”
“Ah, well, sure. You can, um, light my cigarette, if you’re of a mind to.”
“No. There are limits. I mean, a man can put up with only so much without he descends a rung or two on the old evolutionary ladder, which is up your line. Now, I will hold your hand when it’s dark and you’re afraid of the boogeyman and I will tote your gin bottles out after midnight so no one can see but I will not light your cigarette. And that, as they say, is that.”
Departure of the Witches, 1878 by Luis Ricardo Falero.