Question

How do you graph `y=1/3sec((pix)/2+pi/2)` and include two full periods?

Answer 1

Process of transformations

Explanation:

First understand how the graph of sec(x) looks like and graph it.
The first transformation is a vertical shrink by 1/3, you can just multiply the values of the y-axis by 1/3. Second there is a horizontal shrink by 2/`pi`, you can just multiply the x-axis values by 2/`pi`. If you solve for `(pix)/2+pi/2=0` You can see that the phase shift is -1 and move the graph to the left one. Since the period of sec is `2pi` you divide that by the coefficient of x to get the new period. `(2pi)/(pi/2)=4` and you need two periods, so multiply the period by two and graph for 8 along the x-axis.