Final answer:
The standard sinusoidal representation of the phasor v = 5e⁻¹⁸⁰° with the angular frequency ω = 7 rad/s is v(t) = 5cos(7t + 180°).
Step-by-step explanation:
To find the standard sinusoidal representation of the given phasor v = 5e⁻¹⁸⁰°, we must convert the phasor from its exponential form to a sinusoidal function of time. A phasor in exponential form, such as v = Ve⁻ʹᵐᵃ, is equivalent to V cos(ωt + φ). Here, φ represents the phase angle in degrees and V is the amplitude of the sinusoidal wave. In this case, we have an amplitude of 5 and a phase angle of -180° which is equivalent to 180° as the phase angle should be expressed from 0 to 359 degrees. Subsequently, given that ω = 7 rad/s, the standard sinusoidal representation of the phasor is v(t) = 5cos(7t + 180°).