1. Given these sinusoids:
x_{1}(t) = 0.5cos(25t+20°), x_{2}(t)=0.85cos(25t+160°) and x_{3}(t)= 0.81cos(25t-145°)
(a) Subplot the phasors X_{1}, X_{2} and X_{3} corresponding to the thee sinusoidal signals at time t=0 seconds and on the same subplot, show the sum of the phasors X = X_{1}+X_{2}+X_{3}.
(b) On a second subplot, plot the phasor positions of X_{1}, X_{2}, X_{3} 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 X_{1}, X_{2} and X_{3} 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= X_{1}+(- X_{2}) + X_{3}.
At what time t_{0 }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.