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

1 Answer
May 19, 2016

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]}