What is the domain of #f(x)=cscx#?
The question gets much easier if we recall that, by definition, the function you're dealing with is
Being a fraction, we have to make sure that the denominator is non-zero; and since there are no roots or logarithms, it is the only thing we have to study.
The domain of the function will thus be the following set:
The sine function is defined as the projection of a point on the unit circle on the
The only two points which are on both the unit circle and on the
Finally, our answer is ready: we need to exclude from the domain all the points of the form