When I enter the followings commands with Maple 13, I get a result which I cannot understand.

restart;
with(RootFinding):
NextZero(t->cos(t), 0);
NextZero(t->diff(sin(t), t), 0);

1.570796327
FAIL

I expect to get an approximation to Pi/2 in both cases. Why does computing the derivative in the procedure argument change anything?