Question

Every Fourier series is a _______.

A) Trigonometric series

B) Exponential series

C) Power series

D) Logarithmic series​

Answer 1

Every Fourier series is a A) Trigonometric series

Fourier series representation in Trigonometric form

Since sine and cosine can be expressed in exponential form. Thus by manipulating the exponential Fourier series, we can obtain its Trigonometric form.

Answer 2

Answer:

Every Fourier series is a Trigonometric series.

Step-by-step explanation:

• In terms of an infinite sum of sines and cosines, a Fourier series is an expansion of a periodic function. The orthogonality relationships of the sine and cosine functions are used in Fourier series.
• A trigonometric polynomial can be used to represent any smooth periodic function. Your function's Fourier series is finite because it is smooth.