do the range of a sine function and it's corresponding cosecant function ever overlap? if yes, when does it occur? if no, why does it not occur?

Question

do the range of a sine function and it's corresponding cosecant function ever overlap? if yes, when does it occur? if no, why does it not occur?

Answer 1

If sinx = 1 or -1 then the graphs of y = sinx and y = cscx will intersect(i.e., the ranges overlap).   So, the graphs will intersect when

x = π/2 + kπ, where k is any integer.