It is given that \(f(x)=a\sin x+1\) and \(g(x)=3\cos2x\).
\(f(x)\) has a maximum value of 3 and a minimum value of \(-1\). Find the value of \(a\) and state the line of axis for \(f(x)\).[2]
Sketch, on the same axes, the graphs of \(y=f(x)\) and \(y=g(x)\) for \(0\le x\le2\pi\) radians.[3]
Explain why the solutions to the equation \(3\sin^2x+\sin x-1=0\), for \(0\le x\le\pi\) radians, can be found using the graphs in (b).[3]
Hence, state the number of solutions of the equation \(3\sin^2x+\sin x-1=0\) for \(0\le x\le2\pi\) radians.[1]