Question

Use the graph of y = csc x to find all values of x, 0 ≤ x ≤ 2π, for which the following is true. (Enter your answers as a comma-separated list.) csc x is undefined

Answer 1

Cosecant (csc) is defined as the reciprocal of sine, therefore:

`y = cscx \\ y = (1)/(sinx)`.

1/sinx will be undefined when the denominator sinx = 0.

Recalling the unit circle, sinx = 0 at x = 0 ± πn, where n is an integer.

Since the domain x is restricted from (0, 2π), we only consider the values x = 0, x = π, and x = 2π.

Therefore in the domain 0 ≤ x ≤ 2π, y = csc(x) will be undefined at x = 0, x = π, and x = 2π.