It says, state the reciprocal and inverse functions for sin(x) cos(x) and tan(x) would dat just be 1/sin(x) aka csc(x) and so on then for the inverse would it just be sin^-1(x) and so on?

Yes, that should be the case. keep in mind that arcsin(x) is another way to state the inverse sine function. it also applies for arccos(x), arctan(x), arccsc(x), arcsec(x), and arccot(x). e.g for reciprocal is  inverse is  or  as both are equivalent