Answer: (a) \(a=20\), \(b=2\), \(c=-3\). (b) y-intercept \((0,-4)\).

(a) The amplitude is \(|a|\), so \(a=20\).

The period of \(y=\sin bx\), when \(x\) is measured in degrees, is

\(\frac{360^\circ}{b}.\)

Since the period is \(180^\circ\),

\(\frac{360}{b}=180,\)

so

\(b=2.\)

Using the point \((90^\circ,-3)\),

\(-3=20\sin(2\times90^\circ)+c.\)

Since \(\sin180^\circ=0\), this gives

\(c=-3.\)

Thus

\(\boxed{a=20,\quad b=2,\quad c=-3}.\)

(b) The graph is a continuous tangent curve on the given interval, with

\(g(0)=3\tan0^\circ-4=-4.\)

So the y-intercept is

\(\boxed{(0,-4)}.\)