What is the domain of f(x)=5csc(1/3 x)-1 ?

The domain of f(x)=5csc(1/3 x)-1 is 6pin<x<3pi+6pin\lor 3pi+6pin<x<6pi+6pin

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domain of f(x)=5csc(1/3 x)-1

domain

f (x) = 5 csc (\frac{1}{3} x) - 1

6 πn < x < 3 π + 6 πn or 3 π + 6 πn < x < 6 π + 6 πn

Interval Notation

(6 πn, 3 π + 6 πn) \cup (3 π + 6 πn, 6 π + 6 πn)

Solution steps

Take the denominator(s) of

5 csc (\frac{1}{3} x) - 1

and compare to zero:

x = 6 πn, x = 3 π + 6 πn

Periodicity of

5 csc (\frac{1}{3} x) - 1 : 6 π

Combine period:

6 πn \leq x < 6 π + 6 πn

and undefined points.

The domain is

6 πn < x < 3 π + 6 πn or 3 π + 6 πn < x < 6 π + 6 πn

What is the domain of f(x)=5csc(1/3 x)-1 ?
The domain of f(x)=5csc(1/3 x)-1 is 6pin<x<3pi+6pin\lor 3pi+6pin<x<6pi+6pin