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Answer: $$ \sin (x)=P_{T}(x)+E_{T}(x) $$ where $$ E_{T}(x)=-\frac{\sin (\xi)}{6}(x-\pi / 4)^{3} $$ Since $|\sin (x)| \leq 1$ and $\left|(x-\pi / 4)^{3}\right| \leq(\pi / 4)^{3}$ for $x \in[0, \pi / 2]$, it follows that $$ \left|E_{T}(x)\right|=\frac{\pi^{3}}{6 \times 64}=0.08075 $$

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