Consider the following periodic function with period 2?:
F (t) =
F (t + 2 $\pi$) = f (t)
Which of these is the Fourier representation for f (t)?
A) $ \frac{8}{9}+\frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \sin (n t) $
B) $ \frac{8}{9}+\frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \cos (n t) $
C) $ \frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \sin (n t) $
D) $ \frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \cos (n t) $

Question

Consider the following periodic function with period 2?:
F (t) = 
F (t + 2 $\pi$) = f (t)
Which of these is the Fourier representation for f (t)?
A) $ \frac{8}{9}+\frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \sin (n t) $ 
B) $ \frac{8}{9}+\frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \cos (n t) $ 
C) $ \frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \sin (n t) $ 
D) $ \frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \cos (n t) $

Quizplus · Accepted Answer

The Answer of Consider the following periodic function with period 2?:
F (t) = 
F (t + 2 $\pi$) = f (t)
Which of these is the Fourier representation for f (t)?
A) $ \frac{8}{9}+\frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \sin (n t) $ 
B) $ \frac{8}{9}+\frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \cos (n t) $ 
C) $ \frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \sin (n t) $ 
D) $ \frac{8}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{n \pi}{9} \cos (n t) $

Consider the Following Periodic Function with Period 2?: F (T) π\piπ

Consider the Following Periodic Function with Period 2?:
F (T) $\pi$