What is the domain of y=csc(θ) ?

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

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domain of y=csc(θ)

domain

y = csc (θ)

2 πn < θ < π + 2 πn or π + 2 πn < θ < 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 (θ)

and compare to zero:

θ = 2 πn, θ = π + 2 πn

Periodicity of

csc (θ) : 2 π

Combine period:

2 πn \leq θ < 2 π + 2 πn

and undefined points.

The domain is

2 πn < θ < π + 2 πn or π + 2 πn < θ < 2 π + 2 πn

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