(4) Find the coefficients of the half-range even (cosine), odd (sine) and periodic extensions Fourier series for the function: f(x) = cos(3x), x = [0, π] Answer L = π, ao cos = 0, an cos = 0 if n #3, a3 cos if n bn sin = ao per 2(1 + (−1)¹)n (n² - 9)T = - 0 bn per = 0, an per = = 1. 3, b3 sin = 0. 8n (4n² - 9)T =
(4) Find the coefficients of the half-range even (cosine), odd (sine) and periodic extensions Fourier series for the function: f(x) = cos(3x), x = [0, π] Answer L = π, ao cos = 0, an cos = 0 if n #3, a3 cos if n bn sin = ao per 2(1 + (−1)¹)n (n² - 9)T = - 0 bn per = 0, an per = = 1. 3, b3 sin = 0. 8n (4n² - 9)T =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![(4) Find the coefficients of the half-range even (cosine), odd (sine) and periodic
extensions Fourier series for the function:
f(x) = cos(3x), x = [0, π]
Answer
L = π, ao cos = 0, an cos = 0 if n 3, a3 cos = 1.
2(1 + (−1)n)n
(n² - 9)T
if n
bn sin =
ao per
= 0, an per = 0 bn
=
per
3, b3 sin = 0.
=
8n
(4n² - 9) T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c62ea9-2423-4a35-a6cd-74646c6bbd41%2F679dd661-6cbc-4364-a851-8640f2067e43%2F7t5scxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(4) Find the coefficients of the half-range even (cosine), odd (sine) and periodic
extensions Fourier series for the function:
f(x) = cos(3x), x = [0, π]
Answer
L = π, ao cos = 0, an cos = 0 if n 3, a3 cos = 1.
2(1 + (−1)n)n
(n² - 9)T
if n
bn sin =
ao per
= 0, an per = 0 bn
=
per
3, b3 sin = 0.
=
8n
(4n² - 9) T
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