Final answer:
The student's question involves adding two sinusoidal voltage functions to find the total voltage. The solution uses the trigonometric identity that converts sin(wt+90) to cos(wt), simplifying the sum to 20sin(wt) + 20cos(wt).
Step-by-step explanation:
The student's question pertains to calculating the total voltage v(t) for two sinusoidal functions e1(t)=20sin(wt) and e2(t)=20sin(wt+90), where wt represents the angular frequency multiplied by time, and the +90 in e2(t) represents a phase shift of 90 degrees which corresponds to a quarter cycle shift of a sine wave.
To calculate the total voltage v(t), we simply add the functions:
v(t) = e1(t) + e2(t) = 20sin(wt) + 20sin(wt+90)
To further simplify, we can use the trigonometric identity for the sum of two sine waves:
v(t) = 20sin(wt) + 20cos(wt)
This is because sin(wt+90) is equivalent to cos(wt). The result is a new wave that is the summation of the two individual waves and this represents the total voltage.