sympy/sympy — pull request #1899 by skirpichev (2013-03-15 16:26:22+00:00)
Title: Implement is_rational method for trig (and inverse) functions (issue 3215)

http://planetmath.org/encyclopedia/TheoryOfRationalAndIrrationalNumbers.html
and http://en.wikipedia.org/wiki/Transcendental_function says that
there is only trivial exceptional set for exp (and log) function.
Then, same is valid for trigonometric functions.

For example, lets sin(x) = y is algebraic number. Then,
from y = (exp(I*x) - exp(-I*x))/(2*I) (quadratic equation for exp(I*x))
it follows exp(I*x) is an algebraic number. But the
exceptional set for exp() is just {0}, then x should be 0 and,
thus, the exceptional set for sin(x) is {0}.

PS: Tell me, if you think there should be more tests...