Question

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)

Answer 1

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° .