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If I am asked to write out (for example) a third order taylor polynomial for sin(x), does that mean I would write out 3 terms of the series OR to the x^3 term.

x-x^3/3!+x^5/5!

or just

x-x^3/3!

Also, I have a question for the remainder theorem for taylor series (or Lagrange). If I am doing the remainder for a a polynomial for sinx written out as x-x^3/3!, the remainder theorem says use f^n+1(c)(x-a)^n+1/(n+1)!...but for sinx it skips the x^4 term so how would this work? I would assume you would just use the next term: (x^5/5!) but it does not say this anywhere I can find so I am unsure.

Thanks!