Question

How do you find the domain & range for `y=cscx`?

Answer 1

Please see below.

Explanation:

Cosecant function is closely tied to sine function, as it is its reciprocal. If we relate to coordinate plane, while sine function is `y/r`, cosecant function is `r/y` and problem arises when `y->0`, which happens when angle is `0` or `pi` or `2pi`, `3pi`, etc.

Hence, domain of `cscx` is given by

`x!=npi`, where `n` is an integer.

Again as cosecant function is `r/y` and as `r` in `r/y` is always positive and `r>y`, this function is always greater than or equal to `1` or less than or equal to `-1`.

Tis means, it never takes values between `1` and `-1`.

Further, it is equal to `1` when `x=2npi+pi/2` and is equal to `-1` when `x=2npi-pi/2`, where `n` is an integer.

The graph of `cscx` will appear as shown below.

graph{cscx [-10, 10, -5, 5]}