Why Sine and Cosine Are Orthogonal
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YouTubeTexas Little Apple
Why Sine and Cosine Are Orthogonal
This video proves the orthogonality of sine and cosine functions on ([0,pi]). Using product-to-sum identities, the products (sin(mx) sin(nx)) and (cos(mx)cos(nx)) turn into sums of cosine terms. When the frequencies are different, the oscillations cancel perfectly over the interval. That is why cross terms vanish in Fourier series and many ...
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