Analyzing the function below, compare and contrast the two functions in each problem situation. Be sure to use complete sentences in your comparison. Be sure to include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-minimums, and any phase shift between the two graphs.

1. Y=3sin (2x) and Y=3cos (2x)

2. Y=4sin (2x-π) and Y=cos (3x-π/2)

Step-by-step explanation:

1) Y=3sin (2x) and

Y=3cos (2x)

a) Both have same amplitude which is 3.

b) They have same period as they have same angular frequencies which is 2.

c) But their initial phases differ by π / 2 radian or 90°.

2. Y=4sin (2x-π) and

Y=cos (3x-π/2)

a) Their amplitudes are different. One has amplitude of 4 and the other have amplitude of 1.

b) They have different angular frequencies so their time periods too are different.

c) They have different initial phase difference. That differ by 90°.