Sum of sines in phasor form

How to perform the sum in the following equation in phasor form? I mean analytical using matlab.

Equation:

Ax1*Ax2*sin(2*pi*50*t + Theta_a1 + Theta_a2) + Ax1*Ax3*sin(2*pi*50*t + Theta_a3 + Theta_a2)

Answer 1

[Peter O]

You can treat them as the sum of 2 phasors. Assuming they always have equal frequencies then it's a vector sum of the real and imaginary components.

    Sum = Ax1*Ax2*exp(1j*(theta1+theta2-pi/2) +Ax1*Ax3*exp(1j*(theta3+theta2-pi/2)

Notice I shifted the waveforms to cosine to make the real and imaginary components work.

The magnitude and angle of the resulting wave are M=abs(sum) ThetaS = angle(sum) Y = M*cos(2*pi*50*t + ThetaS)

(Typing on mobile so please excuse if there's a typo or sign error)