Cosine is the derivative of sine.

y = sin(x) - Domain: D = ℝ, x, x0, x<> x0 in ℝ, Δx = x − x

_{0, }Δy = f(x)-f(x_{0}).[sin(x)] ’ = f’(x) = lim (Δy/Δx) = lim [f(x

_{0}+Δx)-f(x_{0})]/Δx = cos(x)

Δx→0 Δx→0The derivative of sine, y = sin(x) —by its

conceptual definitionas “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.

"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.”