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

1 Answer
May 13, 2018

Process of transformations


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.