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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

domain of y=tan(x/3)

domain

y = tan (\frac{x}{3})

3 πn \leq x < \frac{3 π}{2} + 3 πn or \frac{3 π}{2} + 3 πn < x < 3 π + 3 πn

Interval Notation

[3 πn, \frac{3 π}{2} + 3 πn) \cup (\frac{3 π}{2} + 3 πn, 3 π + 3 πn)

Solution steps

Take the denominator(s) of

tan (\frac{x}{3})

and compare to zero:

x = \frac{3 π}{2} + 3 πn

Periodicity of

tan (\frac{x}{3}) : 3 π

Combine period:

3 πn \leq x < 3 π + 3 πn

and undefined points.

The domain is

3 πn \leq x < \frac{3 π}{2} + 3 πn or \frac{3 π}{2} + 3 πn < x < 3 π + 3 πn

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