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→0

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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