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Given the following periodic waveform with period

`T=6,f(t)={(20,-1<=t<=1),(0,1<=t<5):}`

. (a) Find the symmetry: Odd only Odd and half-wave Even and half wave No symmetry Half wave only Even only (b) Calculate

`a_(0)`

and

`w_(0)`

才

`a_(0)=,;,\omega _(0)=`

Express

`a_(0)`

to 3 significant digits and give the exact value for

`\omega _(0)`

. Type Pi for

`\pi `

. (c) Which of the following is the Fourier Series expansion for the given function? (zero harmonics are omitted).

```
b_(1)sin((1)/(3)\pi t)+b_(3)sin(\pi t)+b_(5)sin((5)/(3)\pi t)+a_(7)sin((7)/(3)\pi t)
a_(1)cos((1)/(3)\pi t)+a_(3)cos(\pi t)+a_(5)cos((5)/(3)\pi t)+a_(7)cos((7)/(3)\pi t)
a_(0)+a_(1)cos((1)/(3)\pi t)+a_(2)cos((2)/(3)\pi t)+a_(3)cos(\pi t)+a_(4)cos((4)/(3)\pi t)
b_(1)sin((1)/(3)\pi t)+b_(2)sin((2)/(3)\pi t)+b_(3)sin(\pi t)+b_(4)sin((4)/(3)\pi t)
```

(d) Which of the coefficients

`a_(n)`

or

`b_(n)`

are zero? For non-zero coefficients, round to 3 significant digits.

```
a_(n)=
b_(n)=
```