What is the domain of y=-3tan(1/2 x) ?

The domain of y=-3tan(1/2 x) is 2pin<= x<pi+2pin\lor pi+2pin<x<2pi+2pin

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domain of y=-3tan(1/2 x)

domain

y = - 3 tan (\frac{1}{2} x)

2 πn \leq 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

- 3 tan (\frac{1}{2} x)

and compare to zero:

x = π + 2 πn

Periodicity of

- 3 tan (\frac{1}{2} x) : 2 π

Combine period:

2 πn \leq x < 2 π + 2 πn

and undefined points.

The domain is

2 πn \leq x < π + 2 πn or π + 2 πn < x < 2 π + 2 πn

What is the domain of y=-3tan(1/2 x) ?
The domain of y=-3tan(1/2 x) is 2pin<= x<pi+2pin\lor pi+2pin<x<2pi+2pin