Answer:
The period of the given function is [tex]2\pi[/tex]
Step-by-step explanation:
Given : Function [tex]y=1+\tan(\frac{1}{2}x)[/tex]
To find : What is the period of the function?
Solution :
The general form of the tangent function is [tex]f(x)=A+B\tan(Cx)[/tex]
Where, Period of the tangent function is [tex]P=\frac{\pi}{|C|}[/tex]
Now, Compare the general form with the given function.
[tex]y=1+\tan(\frac{1}{2}x)[/tex]
A=1 , B=1 , [tex]C=\frac{1}{2}[/tex]
Period of the function is
[tex]P=\frac{\pi}{|C|}[/tex]
[tex]P=\frac{\pi}{|\frac{1}{2}|}[/tex]
[tex]P=2\pi[/tex]
So, The period of the given function is [tex]2\pi[/tex]
