What is the domain of f(x)=(-1)/(sin(x)) ?

The domain of f(x)=(-1)/(sin(x)) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of f(x)=(-1)/(sin(x))

domain

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

\frac{- 1}{sin ( x )}

and compare to zero:

x = 2 πn, x = π + 2 πn

Periodicity of

\frac{- 1}{sin ( 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

What is the domain of f(x)=(-1)/(sin(x)) ?
The domain of f(x)=(-1)/(sin(x)) is 2pin<x<pi+2pin\lor pi+2pin<x<2pi+2pin