If the fourier coefficient bn of a periodic function is zero, then it must possess ----------- symmetry.
Question
If the fourier coefficient bn of a periodic function is zero, then it must possess ----------- symmetry.
Solution
If the Fourier coefficient bn of a periodic function is zero, then it must possess even symmetry.
Here's why:
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The Fourier series of a function is a way to represent the function as an infinite sum of sine and cosine waves. The coefficients of these waves, an and bn, are called the Fourier coefficients.
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The bn coefficients are associated with the sine terms in the Fourier series. Sine is an odd function, meaning that it is symmetric about the origin.
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If all the bn coefficients are zero, this means that there are no sine terms in the Fourier series.
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Therefore, the function can only be composed of cosine terms, which are even functions.
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Hence, if all the bn coefficients are zero, the function must possess even symmetry.
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