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 yr, cosecant function is ry and problem arises when y0, which happens when angle is 0 or π or 2π, 3π, etc.

Hence, domain of cscx is given by

xnπ, where n is an integer.

Again as cosecant function is ry and as r in ry 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=2nπ+π2 and is equal to 1 when x=2nππ2, where n is an integer.

The graph of cscx will appear as shown below.

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