We will draw the graph of y = cos x and transform the graph of y = cos x to the graph of y = cos (2x + pi/4). Method1 means shift the graph first then shrink the result graph.

Step1. Draw the graph of y = cos x. The five important points of y = cos x in one period are:

x

0

pi/2

pi

3pi/2

2pi

y = cos x

1

0

-1

0

1

Connect these five points smoothly and extended the graph of y = cos x toward right and left.

Step2. Shift the graph of y = cos x left pi/4 units to get the graph of y = cos (x + pi/4)

Step3. Shrink the result graph by shrinking the x-coordinate of each point to half and keep the y-coordinate the same to get the graph of y = cos (2x + pi/4).