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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Definitions:

Neural Messages

The information that is transmitted throughout the nervous system via neurons, using electrical and chemical signals.

Transduction

The conversion of one form of energy into another form, in psychology, the process by which sensory signals are transformed into neural impulses.

Sound Waves

Vibrations that travel through air or another medium and can be heard when they reach a person's or animal's ear.

Night Blindness

A condition that makes it difficult or impossible to see in low light or darkness, due to impaired rod cell function in the retina.