(a) Copy and complete the table of values for the relation \(y = 3 \sin 2x\). x \(o^o\) \(15^o\) \(30^o\) \(45^o\) \(60^o\) \(75^o\) \(90^o\) \(105^o\) \(12...

(a) For each value of \(x\), calculate \(y=3\sin 2x\), correct to 1 decimal place where necessary.

For example, \(3\sin 2(30^\circ)=3\sin60^\circ=2.598\ldots\approx2.6\).

(b) The plotted graph of \(y=3\sin2x\) is shown below. The curve is drawn through the tabulated points, using the stated scales.

(c)(i) \(3\sin2x+2=0\) gives \(y=-2\). Reading the intersection of the curve with \(y=-2\) gives

\[x\approx111^\circ.\]

Hence the truth set is \(\{111^\circ\}\), approximately.

(c)(ii) \(\frac32\sin2x=0.25\). Since \(y=3\sin2x\), this is equivalent to \(y=0.5\). Reading the intersections of the curve with \(y=0.5\) gives

\[x\approx5^\circ\quad\text{or}\quad x\approx85^\circ.\]

Therefore, the truth set is \(\{5^\circ,\ 85^\circ\}\), approximately.