1. Given these sinusoids:

x₁(t) = 0.5cos(25t+20°),   x₂(t)=0.85cos(25t+160°) and   x₃(t)= 0.81cos(25t-145°)

(a)  Subplot the phasors X₁, X₂ and X₃ corresponding to the thee sinusoidal signals at time t=0 seconds and on the same subplot, show the sum of the phasors X = X₁+X₂+X₃.

(b)  On a second subplot, plot the phasor positions of  X₁, X₂, X₃ and X at t=0.04 seconds. How much phase change in degrees does 0.04 seconds correspond to?

(c)  Comment on the relative position of the phasors X₁, X₂ and X₃ on the two plots and annotate plot to indicate how much they have changed position. Use MATLAB to find the amount of rotation.

(d) On a third subplot, find the time domain equivalent sinusoid of the phasor sum Y= X₁+(- X₂) + X₃.

At what time t₀ will the phasor Y first lie on the positive real axis?

(e)  Submit the plot and source code with any pertinent MATLAB output clearly annotated.