Which graph best represents tan (x/2)=y? (PICTURES INCLUDED)

Which graph best represents tan (x/2) = y?

Let's think about this a bit.

$$\\tan\frac{x}{2}=\frac{sin\frac{x}{2}}{cos\frac{x}{2}}=0\\\\
$Well if $sin\frac{x}{2}=0 $ then this will be true $\\\\
\qquad \qquad $NOTE: When $ sin\frac{x}{2}=0, \;\;cos\frac{x}{2}=\pm1\\\\
sin\frac{x}{2}=0 $ when $ \frac {x}{2}=0,\pi,\2pi, 3\pi, .....\\\\
$multiply both sides by 2$\\\\
x=0,2\pi,4\pi,6\pi,........$$

The answer is C.

It is good to remember CPhill's answer but I have given you an explanation.    

It's Graph "C."   The function can be written as ....tan 1/2(x).... where the "1/2" makes the normal period of the tangent graph twice as long......!!!!