Math CentralQuandaries & Queries


Question from rimoshika, a student:

prove that we can't write sinx and cosx as a finite polynomial.

One way to approach this is:

  • a finite polynomial of degree n has at most n points where it crosses the x axis (roots)

  • sin(x) and cos(x) have an infinite number of points where it crosses the x axis (roots).

Walter Whiteley

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