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  1. sin(0) = 0

  2. cos(0) = 1

  3. The function sin(x) is odd because all exponents in its power series are odd.

  4. The function cos(x) is even because all exponents in its power series are even.

  5. The functions sin(x) and and cos(x) are both continuous since they are differentiable.

  6. The derivatives of sin(x) are cyclic with order four.

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