(a) The function f, defined by \(f : x \mapsto a + b \sin x\) for \(x \in \mathbb{R}\), is such that \(f\left(\frac{1}{6}\pi\right) = 4\) and \(f\left(\frac{1}{2}\pi\right) = 3\).

1. Find the values of the constants \(a\) and \(b\).
2. Evaluate \(ff(0)\).

(b) The function g is defined by \(g : x \mapsto c + d \sin x\) for \(x \in \mathbb{R}\). The range of g is given by \(-4 \leq g(x) \leq 10\). Find the values of the constants \(c\) and \(d\).