The periods of trig functions in the form of #asin(btheta+c)+d, acos(btheta+c)+d#, is given by #p=(2pi)/b#.
Here, #b=(2pi)/3# and we have an equation in the form of #y=acos(btheta+c)+d# , so:
#p=(cancel(2pi))/((cancel(2pi))/3)=3#
The amplitude of #asin(btheta+c)+d, acos(btheta+c)+d# is given by #a#. Here, we see #a=1/4#; therefore, our amplitude is #1/4#.
The midline is the horizontal line #y=m# which runs straight through the middle of the graph of the trigonometric function.
#d=0#, so our function isn't shifted up or down at all. Here, our amplitude is #1/4#, meaning that our highest point will only be at #y=1/4# and our lowest point will be at #y=-1/4#.
The line which runs through the middle of this is #y=0#, because #0# lies right in between #-1/4# and #1/4# .
