Solve inequality involving trig

A question is this type if and only if it requires finding the set of values of x (or θ) in a given interval for which a trig expression satisfies an inequality (e.g. cos 2x ≤ 0.5 or 2 cos x + 3 sin x > 0).

1 questions · Moderate -0.8

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OCR C2 2011 June Q9
11 marks Moderate -0.8
9
  1. \includegraphics[max width=\textwidth, alt={}, center]{4d03f4e3-ae6c-4a0d-ae4d-d89258d2919a-4_362_979_1505_625} 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.
    1. State the period of \(y = \cos 2 x\).
    2. State the coordinates of \(A\).
    3. Solve the inequality \(\cos 2 x \leqslant 0.5\) for \(0 \leqslant x \leqslant \pi\), giving your answers exactly.
  2. Solve the equation \(\cos 2 x = \sqrt { 3 } \sin 2 x\) for \(0 \leqslant x \leqslant \pi\), giving your answers exactly.