3. Convert the parametric equations of the cycloid $\left\{\begin{array}{l}x=a(\theta-\sin \theta), \\ y=a(1-\cos \theta)\end{array}(0 \leq \theta \leq \pi, a\right.$ is a positive number $)$, to a Cartesian equation.
3. $\left(x-a \cdot \arccos \left(\frac{a-y}{a}\right)\right)^{2}+(y-a)^{2}=a^{2}$

Analysis: From $\left\{\begin{array}{l}x=a(\theta-\sin \theta) \\ y=a(1-\cos \theta)\end{array}\right.$, we know $\left\{\begin{array}{c}(x-a \theta)^{2}+(y-a)^{2}=a^{2} \\ \theta=\arccos \left(\frac{a-y}{a}\right)\end{array}\right.$, eliminating $\theta$ yields:
$$
\left(x-a \cdot \arccos \left(\frac{a-y}{a}\right)\right)^{2}+(y-a)^{2}=a^{2}
$$