Solve the equation \(\sin x = 0.8\) in the interval \(0 \leqslant x \leqslant 2 \pi\), giving your answers in radians to three significant figures.
The diagram shows the graph of the curve \(y = \sin x , 0 \leqslant x \leqslant 2 \pi\) and the lines \(y = k\) and \(y = - k\).
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The line \(y = k\) intersects the curve at the points \(P\) and \(Q\), and the line \(y = - k\) intersects the curve at the points \(R\) and \(S\).
The point \(M\) is the minimum point of the curve.
Write down the coordinates of the point \(M\).
The \(x\)-coordinate of \(P\) is \(\alpha\).
Write down the \(x\)-coordinate of the point \(Q\) in terms of \(\pi\) and \(\alpha\).
Find the length of \(R S\) in terms of \(\pi\) and \(\alpha\), giving your answer in its simplest form.
Sketch the graph of \(y = \sin 2 x\) for \(0 \leqslant x \leqslant 2 \pi\), indicating the coordinates of points where the graph intersects the \(x\)-axis and the coordinates of any maximum points.