A cosine graph with equation \(y=a\cos bx+c\), where \(x\) is in degrees, has period \(180^\circ\) and has a minimum value of \(-4\) and a maximum value of \(2\). Find the values of the integers \(a\), \(b\) and \(c\).[3]
Sketch, on the axes below, the graph of the curve \(y=4\sin2\theta-1\) for \(0\le\theta\le2\pi\).[3]
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Answer:(a) \(a=\pm3,\ b=\pm2,\ c=-1\) (positive convention: \(3,2,-1\)). (b) Two sine cycles, maximum \(3\), minimum \(-5\).