Determine range or set of values

A question is this type if and only if it asks for the range of a trigonometric function or the set of values of a parameter k for which certain conditions hold (like no solutions).

3 questions · Moderate -0.6

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CAIE P1 2010 June Q11
10 marks Moderate -0.3
The function \(f : x \mapsto 4 - 3\sin x\) is defined for the domain \(0 \leq x < 2\pi\).
  1. Solve the equation \(f(x) = 2\). [3]
  2. Sketch the graph of \(y = f(x)\). [2]
  3. Find the set of values of \(k\) for which the equation \(f(x) = k\) has no solution. [2]
The function \(g : x \mapsto 4 - 3\sin x\) is defined for the domain \(\frac{1}{2}\pi \leq x \leq A\).
  1. State the largest value of \(A\) for which \(g\) has an inverse. [1]
  2. For this value of \(A\), find the value of \(g^{-1}(3)\). [2]
CAIE P1 2011 June Q9
8 marks Moderate -0.3
The function \(f\) is such that \(f(x) = 3 - 4\cos^k x\), for \(0 \leq x \leq \pi\), where \(k\) is a constant.
  1. In the case where \(k = 2\),
    1. find the range of \(f\), [2]
    2. find the exact solutions of the equation \(f(x) = 1\). [3]
  2. In the case where \(k = 1\),
    1. sketch the graph of \(y = f(x)\), [2]
    2. state, with a reason, whether \(f\) has an inverse. [1]
AQA AS Paper 1 2018 June Q3
2 marks Easy -1.2
State the interval for which \(\sin x\) is a decreasing function for \(0° \leq x \leq 360°\) [2 marks]