Sine function/Approximating polynomials/Various conditions/Exercise

Let $f(x)=\sin x$. Determine polynomials $P,Q,R$ of degree $\le 3$, 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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