Answer:
C. [tex]2\pi[/tex]
Step-by-step explanation:
We have been given a trigonometric function [tex]y=1+\text{tan}(\frac{1}{2}x)[/tex]. We are asked to find period of our given function.
We know that period of a tangent function is form [tex]f(x)=a\cdot \text{tan}(bx)+c[/tex], is [tex]\text{Period}=\frac{\pi}{|b|}[/tex].
We can rewrite our given function as:
[tex]y=\text{tan}(\frac{1}{2}x)+1[/tex]
We can see that value of b is [tex]\frac{1}{2}[/tex] for our given function.
[tex]\text{Period}=\frac{\pi}{\frac{1}{2}}[/tex]
Using fraction rule [tex]\frac{a}{\frac{b}{c}}=\frac{ac}{b}[/tex], we will get:
[tex]\text{Period}=\frac{2\pi}{1}[/tex]
[tex]\text{Period}=2\pi[/tex]
Therefore, period of our given function is [tex]2\pi[/tex] and option C is the correct choice.
