Question: adding more properties to elementary functions

Dear all:

    I am wondering if there is any way in Maple to add properties to elementary functions? For example, both

is(sin(x),continuous) assuming x::real;


is(sin(x),monotonic) assuming x>0 and x<Pi/2;

fail. More specifically, how to tell Maple that sin(x) is continuous and monotonic if  k*Pi <= x <= k*Pi + Pi/2 ?

Another question is that I am not very sure how to use the monotonic property, i.e how it can be used to simplify your expression? Can someone give me an example?



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