Sine function/Approximating polynomials/Various conditions/Exercise

Let ${}f(x)=\sin x$. Determine polynomials ${}P,Q,R$ of degree ${}\leq 3$, fulfilling the following conditions.

(a) ${}P$ coincides with ${}f$ at the points ${}-\pi ,0,\pi$.

(b) ${}Q$ coincides with ${}f$ in ${}0$ and in ${}\pi$ up to the first derivative.

(c) ${}R$} coincides with ${}f$ in ${}\pi /2$ up to the third derivative.

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