y = Sin(pi) = 0
Then its derivative is
dy/dx = Cos(pi). = -1
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The anti-derivative of any constant c, is just c*x. Thus, the antiderivative of pi is pi*x. We can verify this by taking the derivative of pi*x, which gives us pi.
The derivative of sin (x) is cos (x). It does not work the other way around, though. The derivative of cos (x) is -sin (x).
d/dx[cos(pi)] = - sin(pi)
One. Exactly one.
It is pi/2 + 2*k*pi radians for integer k.