1 a)
$ x_(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2}) $
Based on the Prof Alen's note page 179
$ x_(f) \,\!= \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))sinc(t/2) $
b)
$ x_(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2}) $
Based on the Prof Alen's note page 179
$ x_(f) \,\!= \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))sinc(t/2) $
