The slopes of the tangent lines of this function are the same for any two points that are separated by a distance of $2\pi$. Find the two points $(x_0,f(x_0))$ and $(x_0+2\pi,f(x_0+2\pi))$ with $0< x_0<2$ whose tangent lines are the same line.
as much as i can calculated I got, that the slope of tangent line is equal to the derivative of $y$, therefore $= \cos x -1/2 = -1/2$
how should i find the points? $y(x_0)=\pi/2-9.5$
$y(x_0+2\pi)=(\pi+19)/2\pi$ or $19/2\pi$?
i was confused here.
could anyone help me please, any help would be appreciated