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Consider the following input $x(t)$ and output $y(t)$ pairs for two different systems.

  1. $x(t)=\sin (t), y(t)=\cos (t),$
  2. $x(t)=t+\sin (t), y(t)=2 t+\sin (t-1).$

Which of these systems could possibly be linear and time invariant? Choose the most appropriate answer from below.

  1. (i), but not (ii).
  2. (ii), but not (i).
  3. both (i) and (ii).
  4. neither (i) nor (ii).
  5. neither, but a system with $x(t)=\sin (2 t), y(t)=\sin (t) \cos (t) \operatorname{could~be.~}$
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