Final answer:
The standard sinusoidal representation of the given phasor v(t) = 13 sin(9t + 90°) V is 13°<9 rad/s with an amplitude of 13 V, an angular frequency of 9 rad/s, and a phase shift of 90°.
Step-by-step explanation:
To find the standard sinusoidal representation of the given phasor with the expression v(t) = 13 sin(9t + 90°) V, we need to identify the amplitude, angular frequency, and phase shift from the equation and express them in their respective sinusoidal form. the amplitude (A) of the phasor is 13 V, which is the coefficient in front of the sine function. The angular frequency (ω) is the coefficient of t inside the sine function, which in this case is 9 rad/s. The phase shift (φ) is represented by the term +90°, which tells us the phase angle at which the sine wave starts, and it must be expressed between 0 to 359 degrees. therefore, the standard sinusoidal representation of the given phasor is v(t) = 13 sin(9t + 90°) V = 13°<9 rad/s.
It's worth noting that the phasor representation is a way to simplify the analysis of sinusoidal functions by treating them as vectors in the complex plane, which rotate with an angular frequency (ω) and have an amplitude corresponding to their magnitude.