Question

The trigonometric Fourier series of an even function of time does not have:

• A. The de term
• B. The cosine terms
• C. The sine terms
• D. The odd harmonic terms

Hint:

In the Fourier series of an even function, the sine terms are always absent, and only cosine terms and possibly a constant term are present.

Answer 1

The Correct Option is C

The Fourier series of an even function of time contains only cosine terms and possibly the constant (de) term. This is because:
- The Fourier series expansion of an even function only involves even functions of time, which means the sine terms (which are odd functions) will vanish.
- An even function is symmetric about the vertical axis, so its Fourier series representation will not have sine terms (which are odd functions).
Thus, the correct answer is that the Fourier series of an even function does not have sine terms, which corresponds to option (3).