Consider the unit vectors \(\hat{\mathbf{x}}, \hat{\mathbf{y}}, \hat{\mathbf{r}}\), and \(\hat{\boldsymbol{\theta}}\) in a plane.

(a) Find \(\hat{\mathbf{r}}\) and \(\hat{\boldsymbol{\theta}}\) in terms of any or all of \(\hat{\mathbf{x}}, \hat{\mathbf{y}}, x\), and \(y\).

(b) Find \(\hat{\mathbf{x}}\) and \(\hat{\mathbf{y}}\) in terms of any or all of \(\hat{\mathbf{r}}, \hat{\boldsymbol{\theta}}, r\), and \(\theta\).