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

1 Answer
Aug 4, 2018

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Please read the explanation.

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=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.

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Graph the given trigonometric function:

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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.