Solve p(trig(θ)) = 0

Questions where you solve p(sin θ) = 0, p(cos θ) = 0, or p(tan θ) = 0 by first solving p(x) = 0, then solving the resulting trigonometric equations for θ in a given interval.

1 questions · Moderate -0.3

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Edexcel C2 Q7
11 marks Moderate -0.3
$$f(x) = 2x^3 - 5x^2 + x + 2.$$
  1. Show that \((x - 2)\) is a factor of \(f(x)\). [2]
  2. Fully factorise \(f(x)\). [4]
  3. Solve the equation \(f(x) = 0\). [1]
  4. Find the values of \(\theta\) in the interval \(0 \leq \theta \leq 2\pi\) for which $$2\sin^3 \theta - 5\sin^2 \theta + \sin \theta + 2 = 0,$$ giving your answers in terms of \(\pi\). [4]