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

 

A-

 

 

 

B-

 

 

 

 

C-

 

 

 

 

D-

Guest Oct 3, 2014

Best Answer 

 #2
avatar+94105 
+5

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.    

Melody  Oct 5, 2014
 #1
avatar+92673 
+5

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
avatar+94105 
+5
Best Answer

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.    

Melody  Oct 5, 2014

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