What is the domain of csc(x) ?

The domain of csc(x) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of csc(x)

domain

csc (x)

2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

Interval Notation

(2 πn, π + 2 πn) \cup (π + 2 πn, 2 π + 2 πn)

Solution steps

Take the denominator(s) of

csc (x)

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

csc (x) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn < x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

f (x) = 7.5 x + 1500

x^{2} + 2 x - 3

\frac{x ^{2}}{x ^{2} - 1}

\frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9}

(- 3, 4), (- 6, - 1)

What is the domain of csc(x) ?
The domain of csc(x) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin