Question

How many period s of the function are there between

Answer 1

The period of a tangent function y = atan(bx) is the distance between any two consecutive vertical asymptotes. And it is given by:

`period=(\pi)/(|b|)`

So, given the function y = tan x, we have that b = 1, therefore the period is:

`\text{period}=(\pi)/(|1|)=\pi`

Next, between the given points:

`\begin{gathered} -(5\pi)/(2)=-2.5\pi \\ and \\ (7\pi)/(2)=3.5\pi \end{gathered}`

There are:

`3.5\pi-(-2.5\pi)=6\pi`

Since the period is π, so:

`(6\pi)/(\pi)=6`

Answer: 6