What is the domain of y=csc(x)+1 ?

The domain of y=csc(x)+1 is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of y=csc(x)+1

domain

y = csc (x) + 1

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) + 1

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

csc (x) + 1 : 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

What is the domain of y=csc(x)+1 ?
The domain of y=csc(x)+1 is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin