The area of the shaded region is given by \(\int _ { 0 } ^ { 2 } \sin x \mathrm {~d} x\), where \(x\) is in radians.
Use the trapezium rule with five ordinates (four strips) to find an approximate value for the area of the shaded region, giving your answer to three significant figures.
Describe the geometrical transformation that maps the graph of \(y = \sin x\) onto the graph of \(y = 2 \sin x\).
Use a trigonometrical identity to solve the equation
$$2 \sin x = \cos x$$
in the interval \(0 \leqslant x \leqslant 2 \pi\), giving your solutions in radians to three significant figures.