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The diagram shows part of the curve \(y = \cos 2 x\), where \(x\) is in radians. The point \(A\) is the minimum point of this part of the curve.
State the period of \(y = \cos 2 x\).
State the coordinates of \(A\).
Solve the inequality \(\cos 2 x \leqslant 0.5\) for \(0 \leqslant x \leqslant \pi\), giving your answers exactly.
Solve the equation \(\cos 2 x = \sqrt { 3 } \sin 2 x\) for \(0 \leqslant x \leqslant \pi\), giving your answers exactly.