QuestionFind a parametrization of the sphere $x^{2}+y^{2}+z^{2}=a^{2}$.

Studdy Solution
Verify that the parametrization covers the entire sphere by varying $\theta$ from $0$ to $\pi$ and $\phi$ from $0$ to $2\pi$.
The parametrization of the sphere $x^2 + y^2 + z^2 = a^2$ is: $$\mathbf{r}(\theta, \phi) = (a \sin(\theta) \cos(\phi), a \sin(\theta) \sin(\phi), a \cos(\theta)), \quad \theta \in [0, \pi], \ \phi \in [0, 2\pi]$$