What is the domain of 3csc(x/2) ?

The domain of 3csc(x/2) is 4pin<x<2pi+4pin\lor 2pi+4pin<x<4pi+4pin

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domain of 3csc(x/2)

domain

3 csc (\frac{x}{2})

4 πn < x < 2 π + 4 πn or 2 π + 4 πn < x < 4 π + 4 πn

Interval Notation

(4 πn, 2 π + 4 πn) \cup (2 π + 4 πn, 4 π + 4 πn)

Solution steps

Take the denominator(s) of

3 csc (\frac{x}{2})

and compare to zero:

x = 4 πn, x = 2 π + 4 πn

Periodicity of

3 csc (\frac{x}{2}) : 4 π

Combine period:

4 πn \leq x < 4 π + 4 πn

and undefined points.

The domain is

4 πn < x < 2 π + 4 πn or 2 π + 4 πn < x < 4 π + 4 πn

f (x) = \frac{2}{x - 4} + \frac{1}{x + 2}

f (x) = \frac{x - 3}{x ^{2} - x - 6}

f (x) = \frac{3}{x + 2} + 1

f (x) = (\frac{2}{x + 1}) (\frac{x}{x + 1})

f (x) = 3 x + 15

What is the domain of 3csc(x/2) ?
The domain of 3csc(x/2) is 4pin<x<2pi+4pin\lor 2pi+4pin<x<4pi+4pin