Answer
The answer is $y=x-2 \pi+8$.
Work Step by Step
According to Eq.(7) the cycloid generated by a circle of radius 4 has parametric equations
$x(t)=4 (t-\sin t)$, $y(t)=4(1-\cos t)$.
Using Eq.(8) the slope of the tangent line to the cycloid is
$dy/dx=y'(t)/x'(t)=4\sin t/4(1-\cos t)=\sin t/(1-\cos t)$.
Since $c(\pi/2)=(2\pi-4,4)$ and $\frac{dy}{dx}|_{t=\pi /2 }=1$. The equation of the tangent line at $t=\pi/2$ is
$y-4=x-(2 \pi-4)$,
$y=x-2 \pi+8$.
