A pendulum maker compares the arc x with the straight height sin x for a small angle x in radians…

Step 1. The top. $x - \sin x = x - \left(x - \dfrac{x^3}{6} + \dfrac{x^5}{120} - \dots\right) = \dfrac{x^3}{6} - \dfrac{x^5}{120} + \dots$

Step 2. Divide by $x^3$. $Q(x) = \dfrac{1}{6} - \dfrac{x^2}{120} + \dots$ As $x \to 0$ this tends to $\dfrac{1}{6} \approx 0.1667$.

Step 3. At $x = 0.5$. $\sin 0.5 = 0.479426$, so $Q(0.5) = \dfrac{0.5 - 0.479426}{0.125} = 0.1646$.