Question

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

Answer 1

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Please read the explanation.

Explanation:

`" "`
`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=1/2`

`rArr 2pi`

x-scale: `color(blue)("Period"/2)`

`rArr (2pi)/2=pi`

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

For the sake of focus and clarity contraint is used.

Graph the given trigonometric function:

Note:

1. Constraint `-2 pi < x < 2pi`

2. Parent graph of `y=f(x)=tan(x)` is also available in color `color(red)("RED")` for comparison

3. Graph of the given function `y=f(x)=[tan(x/2)]` is in `color(blue)("BLUE"`

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

Hope you find this useful.