Solve the equation \(\cos x = 0.3\) in the interval \(0 \leqslant x \leqslant 2 \pi\), giving your answers in radians to three significant figures.
The diagram shows the graph of \(y = \cos x\) for \(0 \leqslant x \leqslant 2 \pi\) and the line \(y = k\).
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The line \(y = k\) intersects the curve \(y = \cos x , 0 \leqslant x \leqslant 2 \pi\), at the points \(P\) and \(Q\). 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 \(Q\) in terms of \(\pi\) and \(\alpha\).
Describe the geometrical transformation that maps the graph of \(y = \cos x\) onto the graph of \(y = \cos 2 x\).
Solve the equation \(\cos 2 x = \cos \frac { 4 \pi } { 5 }\) in the interval \(0 \leqslant x \leqslant 2 \pi\), giving the values of \(x\) in terms of \(\pi\).
(4 marks)