Explanation:




Fourier Series:


The Fourier series represents a periodic function as a sum of sinusoidal functions. It is used to decompose a periodic function into a series of simple sine and cosine functions. The trigonometric Fourier series is commonly used to represent periodic functions in terms of sine and cosine terms.




Even Function:


An even function is a function that is symmetric about the y-axis. Mathematically, an even function can be represented as:




f(t) = f(-t)




Sine Terms:


Sine terms in the trigonometric Fourier series represent odd harmonics. An odd harmonic is a sinusoidal function with a frequency that is an odd multiple of the fundamental frequency. Sine terms have a phase shift of 90 degrees and are used to represent odd functions.




Odd Harmonic Terms:


Odd harmonic terms in the trigonometric Fourier series are represented by sine terms. These terms are used to represent odd functions. An odd function is a function that satisfies the condition:




f(-t) = -f(t)




DC Term:


The DC term in the trigonometric Fourier series represents the average value of the periodic function. It is a constant term that does not depend on the frequency. The DC term is given by the formula:




DC = (1/T) * ∫f(t) dt




Cosine Terms:


Cosine terms in the trigonometric Fourier series represent even harmonics. An even harmonic is a sinusoidal function with a frequency that is an even multiple of the fundamental frequency. Cosine terms have a phase shift of 0 degrees and are used to represent even functions.




Conclusion:


Since an even function is symmetric about the y-axis and does not have any odd harmonics, the trigonometric Fourier series of an even function does not have sine terms. Therefore, option 'A' is the correct answer.