Solution assignment 03 Tangent line to graph

Calculate the slope of the tangent line at the point $P(\displaystyle\frac{\pi}{2},1)$ of the graph of the function:

$y=\sin(x)$

First we calculate the derivative $y'$ :

$y'=\cos(x)$

In the point $(\displaystyle\frac{\pi}{2},1)$ the derivative has the value:

$y'=\cos(\displaystyle\frac{\pi}{2})=0$

and thus the slope of the tangent line at:

$(\displaystyle\frac{\pi}{2},1)$

equals $0$ .