Final answer:
To represent the student's equation as a single phasor, each cosine term is converted into a rotating vector and the resulting amplitude and phase angle are determined by vector addition in the complex plane. The magnitude and angle of the resultant vector provide the values for A and φ in the phasor form x(t) = A cos(wt + φ).
Step-by-step explanation:
The student has provided the equation x(t) = 2 cos(wt+5) + 8 cos(wt+9) + 4 cos(wt) and asked for it to be represented as a single phasor in the form of x(t) = A cos(wt + φ). Phasor addition involves combining these individual cosine terms, each representing a rotating vector (phasor), into one resulting vector. This resulting vector is then described by its amplitude A and phase angle φ in the phasor representation.
The individual terms can be represented by vectors in the complex plane, and their vector sum gives us the resultant vector. To do this, we convert each cosine term to its equivalent exponential form using Euler's formula, add the vectors, and then convert the result back to the cosine form to find the values for A and φ.
The process involves calculating the real and imaginary components of each phasor, adding them together to find the resultant phasor's magnitude and angle (φ), which will give us the desired representation of the signal x(t).