What is the slope of the tangent line to g(x)=cos(x+pi) at x=pi

This was answerd just a day or two ago:

 

remember    cos(x+pi) = -cos(x)

 

d/dx (-cos(x)) = sinx      and at pi    sin(x) = 0

The slope of the line tangent to a curve at a point is just the derivative of that curve evaluated at the point.

 

\(g(x) = \cos(x+\pi)\\ \dfrac{dg}{dx}(x) = -\sin(x+\pi)\\ \dfrac{dg}{dx}(\pi) = -\sin(\pi + \pi) = \\ \sin(2\pi) = 0\\ \text{hence the slope of the line tangent to }g(x) \text{ at }x=\pi \text{ equals }0.\)