#2**+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**+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**+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