Draw the graph of y = cos (2x + pi/4) (method1)
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).