Deduce related equation solution

A question is this type if and only if it asks to use solutions from a previous part to deduce solutions to a related equation (e.g., changing sign or argument).

2 questions · Standard +0.6

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Edexcel C3 2016 June Q3
10 marks Standard +0.8
  1. (a) Express \(2 \cos \theta - \sin \theta\) in the form \(R \cos ( \theta + \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\). Give the exact value of \(R\) and give the value of \(\alpha\) to 2 decimal places.
    (b) Hence solve, for \(0 \leqslant \theta < 360 ^ { \circ }\),
$$\frac { 2 } { 2 \cos \theta - \sin \theta - 1 } = 15$$ Give your answers to one decimal place.
(c) Use your solutions to parts (a) and (b) to deduce the smallest positive value of \(\theta\) for which $$\frac { 2 } { 2 \cos \theta + \sin \theta - 1 } = 15$$ Give your answer to one decimal place.
Edexcel C34 2016 June Q1
9 marks Standard +0.3
  1. (a) Express \(3 \cos \theta + 5 \sin \theta\) in the form \(R \cos ( \theta - \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\). Give the exact value of \(R\) and give the value of \(\alpha\) to 2 decimal places.
    (b) Hence solve, for \(0 \leqslant \theta < 360 ^ { \circ }\), the equation
$$3 \cos \theta + 5 \sin \theta = 2$$ Give your answers to one decimal place.
(c) Use your solutions to parts (a) and (b) to deduce the smallest positive value of \(\theta\) for which $$3 \cos \theta - 5 \sin \theta = 2$$
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