Chapter 4: Systems Based on Numbers

Section 6: Mathematical Functions

Two sine functions

Sin[a x] + Sin[b x] can be rewritten as 2 Sin[(a + b)/2 x] Cos[(a - b)/2 x] (using TrigFactor), implying that the function has two families of equally spaced zeros: 2 π n/(a + b) and 2 π (n + 1/2)/(b - a) .

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From Stephen Wolfram: A New Kind of Science [citation]