# How do you graph y=tan((1/2)x)?

Aug 4, 2018

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#### Explanation:

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color(red)(y=f(x)=[tan(x/2)]

Let us look at the standard form:

color(blue)(y=f(x)=a*tan(bx-c)+d

color(green)(a=1, b=1/2, c=0 and d=0

Period : color(red)(pi/b, with $b = \frac{1}{2}$

$\Rightarrow 2 \pi$

x-scale: $\textcolor{b l u e}{\frac{\text{Period}}{2}}$

$\Rightarrow \frac{2 \pi}{2} = \pi$

Let us look at the data table, with constraint $- 2 \pi < x < 2 \pi$

For the sake of focus and clarity contraint is used.

Graph the given trigonometric function:

Note:

1. Constraint $- 2 \pi < x < 2 \pi$

2. Parent graph of $y = f \left(x\right) = \tan \left(x\right)$ is also available in color $\textcolor{red}{\text{RED}}$ for comparison

3. Graph of the given function $y = f \left(x\right) = \left[\tan \left(\frac{x}{2}\right)\right]$ is in color(blue)("BLUE"

4. x-intercepts : They happen within the periods of $2 \pi$
i.e., $\left(- 4 \pi , - 2 \pi , 0 , 2 \pi , 4 \pi\right)$ etc

Hope you find this useful.