Does Shifting Time Reference in AC Circuits Help Simplify Functions?

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Shifting the time reference in AC circuits simplifies the analysis of voltage and current functions. By rewriting the voltage function from Vmcos(ωt + θ) to Vmsin(ωt + θ), the discussion highlights the transformation of cosine to sine, which aids in applying Euler's identity. Multiplying the forcing function by j converts the cosine function into a sine function, facilitating the use of complex numbers in circuit analysis. The superposition theorem is then employed to combine the responses of the transformed functions. This method ultimately clarifies the relationship between voltage and current in AC circuits.
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In class we've been talking about circuits with AC sources of the form v(t) = Vmcos(ωt+θ) which produces a current i(t) = Imcos(ωt+Φ). They go on to talk about shifting their time reference by re-writing the function for voltage, Vmcos(ωt + θ - 90°) = Vmsin(ωt+θ) the current Imcos(ωt+Φ-90°) = Imsin(ωt+Φ) for some reason of which I can only speculate. Next multiplication of the forcing function vm(t) by j somehow transforms what was once Vmcos(ωt+θ) into jVmsin(ωt + θ). And then use the superposition theorem to produce the total response for the complex forcing function to be v(t) = Vmcos(ωt+θ) + jVmsin(ωt+θ).
My confusion deals with their "shifting of the reference time" and how they transformed the forcing function into a sinusoid. Do they re-write cosines as sines just to use eulers identity later on?
 
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