Solve the Problem $f ( t ) = 3 t$ On the Interval

question 12

Multiple Choice

Solve the problem.
-Find the nth-order Fourier approximation to the function $f ( t ) = 3 t$ on the interval $[ 0,2 \pi ]$ .

• A) \(\pi - \cos ( t ) - \cos ( 2 t ) - \cos ( 3 t ) - \ldots - \frac { 6 } { n } \cos ( n t )\)
• B) \(3 \pi - 6 \cos ( t ) - 3 \sin ( 2 t ) - 2 \cos ( 3 t ) - \ldots - \frac { 6 } { n } \cos ( n t )\)
• C) \(3 \pi - 6 \sin ( t ) - 3 \sin ( 2 t ) - 2 \sin ( 3 t ) - \ldots - \frac { 6 } { n } \sin ( n t )\)
• D) \(3 \pi - 6 \sin ( t ) - 3 \sin ( 2 t ) - 1 \sin ( 3 t ) - \ldots - \frac { 3 } { n } \sin ( n t )\)

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