HW 8 Solutions: Kudeki and Munson book, Chapter 6, problems 6.2  instead of using the example as given where
the formula to be simplified was obtained from f(t)=sin t  derive the equivalent formula for f(t)=cos t and simplify it.
6.4, 6.5, 6.6, 6.7, 6.8, 6.9, 6.12
6.2
Using the time shift property to find the Fourier coefficients:
1 2
1 2
2
2
1 2
1 2
21
cos
sin
2
1
1
1
by time shift property
2
1
2
1
2
1
1
1
2
1
2
1
2
rewriting
in rectangular form
1:
1
1
1
1
2
1
2
j
n
j
n
jn
n
j
n
j
n
jn
n
j
n
n
f t
t
t
ee
Fe
nn
e
F
n
2
2
2
1
1
12
since 2
1 is always odd,
1
1
1
2
2
1
1
1
11
2
1
2
1
2
1
2
1
2
1
14
2
,
2
,
n
n
n
n
n
n
n
n
n
F
n
n
n
n
F
n
n odd
n
F
n even
n
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 Fall '07
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 Fourier Series, Sin, Trigraph, Emoticon, ej2nt dt

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