Now with a dashed line, see if you can set the amplitude "A" and phase shift "p" that matches the sum.
9
Expression 10: "Y" left parenthesis, "t" , right parenthesis equals "A" cosine left parenthesis, "w" "t" minus "p" , right parenthesisYt=Acoswt−p
10
Expression 11: "p" equals negative 0.5p=−0.5
negative 10−10
1010
11
Expression 12: "A" equals 2.2 4A=2.24
00
1010
12
Here is the actual sum graphed with a solid line. Note that you might need to choose the arctan value in the third or forth quadrant by adding "Pi" to the phase shift.
13
Expression 14: "Z" left parenthesis, "x" , right parenthesis equals StartRoot, left parenthesis, "k" squared plus "k" squared , right parenthesis , EndRoot cosine left parenthesis, "w" times "x" minus left parenthesis, arctan left parenthesis, StartFraction, "k" Subscript, 2 , Baseline Over "k" Subscript, 1 , Baseline , EndFraction , right parenthesis plus "N" pi , right parenthesis , right parenthesisZx=k21+k22cosw·x−arctank2k1+Nπ