Sketch one complete period of y 12 cos 12 x pi4 Label thex

Sketch one complete period of y = 1/2 cos (1/2 x - pi/4). Label the-x intercepts and minimum points using ordered pairs. State the amplitude, period, and phase shift. What is the range of this function?

Solution

y=(1/2)cos(x/2-pi/4)

This expression is of the form y=Acos(BX-C)

where A is the amplitude which is 1/2 here

Period =2pi/B= 2pi/1/2 =4pi

Phase shift=C/B=pi/4/1/2=pi/2