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

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

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B-

C-

D-

Guest Oct 3, 2014

#2
+92206
+5

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

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

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

Melody  Oct 5, 2014
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#1
+85681
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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......!!!!

CPhill  Oct 3, 2014
#2
+92206
+5

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

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