For what numbers x, -2π≤ x ≤ 2π, does the graph of y = tan x have vertical asymptotes.?

A given function will have vertical asymptotes when its denominator becomes equal to zero.

Particularly, we know that:

tan(x) =  sin(x)/cos(x)

So the x-values of the asymptote are the values of x such that:

cos(x)  = 0

We know that the two zeros in the range [0, 2π] are:

cos(π/2) = 0

cos(3π/2) = 0

And the cosine function is an even function, which means that:

cos(x) = cos(-x)

So to extend to the range [-2π, 2π] we can use that property:

cos(π/2) = cos(-π/2) = 0

cos(3π/2) = cos(-3π/2) = 0

Then the four x-values of the asymptotes are:

{-3π/2, -π/2, π/2, 3π/2}

Below you can see the graph of the function tan(x)

If you want to learn more about trigonometric functions, you can read:

link

{-3π/2, -π/2, π/2, 3π/2}

Step-by-step explanation:

The basic graph of the function y = tan x on -π/2 ≤ x ≤ π/2 is constrained by the asymptotes x = -π/2 (on the left) and x = π/2 (on the right.  The period of the tangent function is π, so the first vertical asymptote to the left of x = -π/2 is x = -3π/2 and the first to the right of x = π/2 is 3π/2.

In summary, the vertical asymptotes of y = tan x between -2π ≤ x ≤ 2π are {-3π/2, -π/2, π/2, 3π/2}

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.