Implement 3rd harmonic using trigonometric identity#10
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Updated `ds3()` in `sp_fourier_synthesizer.bngl` to use the exact derivative of the 3rd harmonic trigonometric identity instead of an approximation. Cleaned up corresponding comments. Co-authored-by: akutuva21 <44119804+akutuva21@users.noreply.github.com>
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Reviewed in sequence. 3rd-harmonic derivative update is mathematically consistent with the stated identity and improves correctness.
Replaced the hack/approximation in
sp_fourier_synthesizer.bnglwith an implementation of the 3rd harmonic based on the trigonometric identity:sin(3x) = 3*sin(x) - 4*sin^3(x). By taking the derivative,d(sin(3x))/dt = 3*cos(x)*w - 12*sin^2(x)*cos(x)*w, which corresponds in the BNGL functions to3*ds1() - 12*s1()*s1()*ds1(). Theds3()function definition and comments were updated accordingly.PR created automatically by Jules for task 1254867357569153273 started by @akutuva21