f(x) O! f(x)= @ f(x) = f(x) = = # 0 < x < T " , π < x < 2π, and has period 2π 1 1 sin x + sin 3x + sin 5x + +...] 1 1 + cos x + cos 3x + cos 5x + +...] 4 32 52 1 + sin æ+sin 2x +sin 3r+sin 4a - sin 4x +... -{sin x +sin 2r+sin 3x + ...} 2 2 3 $ { π-x 0 1 2 2 ㅠ = | N

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 52E
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Question
Determine the Fourier Series of
π - x
0<x<T
7
=
0
, π < x < 2π, and has period 2
O!
1
2
1
f(x) = sina+sin 3r + sin 5a
3x 5x +
2
ㅠ
@
1
1
f(x)= +
4
2²2 [cos ar + √2 cos 3x + 2 cos 5x +...]
x
3²
52
1
1
1
+ sin x + + sin 2x + sin 3x + sin 4x +
...
2
3
4
π
1
1
f(x)
sin x +
sin 2x + sin 3x +
2
2
3
O $
f(x) = 3 -
-
cos x + 3 cos 3x + cos 5x +
sin x + sin 2x + sin 3x +
#
=
-
cal
-}
]
]
Transcribed Image Text:Determine the Fourier Series of π - x 0<x<T 7 = 0 , π < x < 2π, and has period 2 O! 1 2 1 f(x) = sina+sin 3r + sin 5a 3x 5x + 2 ㅠ @ 1 1 f(x)= + 4 2²2 [cos ar + √2 cos 3x + 2 cos 5x +...] x 3² 52 1 1 1 + sin x + + sin 2x + sin 3x + sin 4x + ... 2 3 4 π 1 1 f(x) sin x + sin 2x + sin 3x + 2 2 3 O $ f(x) = 3 - - cos x + 3 cos 3x + cos 5x + sin x + sin 2x + sin 3x + # = - cal -} ] ]
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