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The Fourier series of a periodic function f (x) is given by 00 6 + 2 1 -cos(nx) + sin(nx). 6" n=1 nº The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 2 -sin(2x). 64 1 1) F(x) = –cos x + 2 sin x + 6. 1 -cos(2x) + 36 1 2) F(x) = 6 + cos x + 2 sin x + 6. 1 -cos(2x) + 36 -sin(2x). 64 1 cos(2x) + 2 -sin(2x). 3) F(x) 64

The Fourier series of a periodic function f (x) is given by 00 6 + 2 1 -cos(nx) + sin(nx). 6" n=1 nº The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 2 -sin(2x). 64 1 1) F(x) = –cos x + 2 sin x + 6. 1 -cos(2x) + 36 1 2) F(x) = 6 + cos x + 2 sin x + 6. 1 -cos(2x) + 36 -sin(2x). 64 1 cos(2x) + 2 -sin(2x). 3) F(x) 64

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 22E
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The Fourier series of a periodic function f (x) is given by 1 6 + 2 – + (xu)soɔ- n6 2 sin(nx). n=1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 1 -cos(2x) + 36 Cos(2r) + 36 cos(2r) + sin(2r). 1) F(x) = -cos x + 2 sin x + 6. -sin(2x). 64 1 2) F(x) = 6 + cos x + 2 sin x + 1 2 -sin(2x). 64 1 3) F(x) -cos(2x) + sin(2x). 36 64
Transcribed Image Text:The Fourier series of a periodic function f (x) is given by 1 6 + 2 – + (xu)soɔ- n6 2 sin(nx). n=1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 1 -cos(2x) + 36 Cos(2r) + 36 cos(2r) + sin(2r). 1) F(x) = -cos x + 2 sin x + 6. -sin(2x). 64 1 2) F(x) = 6 + cos x + 2 sin x + 1 2 -sin(2x). 64 1 3) F(x) -cos(2x) + sin(2x). 36 64
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