Question

What is the period of y=1+tan(1/2x)?

Answer 1

periodic in x  and 2Pi is the period

Answer 2

The period of the given function is
`2\pi`

Explanation:

Given : Function
`y=1+\tan((1)/(2)x)`

To find : What is the period of the function?

Solution :

The general form of the tangent function is
`f(x)=A+B\tan(Cx)`

Where, Period of the tangent function is
`P=(\pi)/(|C|)`

Now, Compare the general form with the given function.

`y=1+\tan((1)/(2)x)`

A=1 , B=1 ,
`C=(1)/(2)`

Period of the function is

`P=(\pi)/(|C|)`

`P=(\pi)/(|(1)/(2)|)`

`P=2\pi`

So, The period of the given function is
`2\pi`