16. Use the De Moivre formulas (11) to derive the standard formulas for cos (0 + 6) and sin (0 + ø). THE COMPLEX FORM OF THE FULL FOURIER SERIES The eigenfunctions of -d²/dx² on (-1, 1) with the periodic boundary conditions are sin(nлx/l) and cos(nëx/l). But recall the DeMoivre formulas, which express the sine and cosine in terms of the complex exponentials: eie -i0 - e ei te -i0 sin 0 and cos 0: = 2i 2 (11)
16. Use the De Moivre formulas (11) to derive the standard formulas for cos (0 + 6) and sin (0 + ø). THE COMPLEX FORM OF THE FULL FOURIER SERIES The eigenfunctions of -d²/dx² on (-1, 1) with the periodic boundary conditions are sin(nлx/l) and cos(nëx/l). But recall the DeMoivre formulas, which express the sine and cosine in terms of the complex exponentials: eie -i0 - e ei te -i0 sin 0 and cos 0: = 2i 2 (11)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 31E
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