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:

$period=\frac{\pi}{|b|}$

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

$\text{period}=\frac{\pi}{|1|}=\pi$

Next, between the given points:

$\begin{gathered} -\frac{5\pi}{2}=-2.5\pi \\ and \\ \frac{7\pi}{2}=3.5\pi \end{gathered}$

There are:

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

Since the period is π, so:

$\frac{6\pi}{\pi}=6$

Answer: 6