Final answer:
The exponential Fourier series of cos(t) can be expressed as a sum of weighted complex exponential functions. The general form of the exponential Fourier series is cos(t) = A0/2 + Σ(Ak * cos(k * t) + Bk * sin(k * t)). The coefficients Ak and Bk can be determined using integrals.
Step-by-step explanation:
The exponential Fourier series of cos(t) can be expressed as a sum of weighted complex exponential functions. The general form of the exponential Fourier series is given by:
Euler's formula can be used to express the complex exponential functions in terms of sine and cosine functions. Therefore, the exponential Fourier series of cos(t) is:
cos(t) = A0/2 + Σ(Ak * cos(k * t) + Bk * sin(k * t))
The coefficients Ak and Bk can be determined by using the formulas:
Ak = (2/T) * ∫[0,T] cos(t) * cos(k * t) dt
Bk = (2/T) * ∫[0,T] cos(t) * sin(k * t) dt
where T is the period of the function (in this case, T = 2π). The integral can be evaluated to find the values of Ak and Bk for each value of k.