  In this sequel to our recent note it is shown, in a unified manner, by making
use of some basic properties of certain special functions, such as the Hurwitz
zeta function, Lerch zeta function and Legendre chi function, that the values
of all derivatives of four trigonometric functions at rational multiples of
$\pi$ can be expressed in closed form as simple finite sums involving the
Bernoulli and Euler polynomials. In addition, some particular cases are
considered.
