Deduce solutions from earlier result

A question is this type if and only if it asks the student to use solutions already found in a previous part to write down (without re-solving) the solutions of a related equation obtained by a substitution such as replacing θ with nθ + c.

2 questions · Standard +0.0

1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
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CAIE P1 2013 November Q4
6 marks Moderate -0.3
4
  1. Solve the equation \(4 \sin ^ { 2 } x + 8 \cos x - 7 = 0\) for \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).
  2. Hence find the solution of the equation \(4 \sin ^ { 2 } \left( \frac { 1 } { 2 } \theta \right) + 8 \cos \left( \frac { 1 } { 2 } \theta \right) - 7 = 0\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
Edexcel Paper 2 Specimen Q12
8 marks Standard +0.3
  1. (a) Solve, for \(- 180 ^ { \circ } \leqslant x < 180 ^ { \circ }\), the equation
$$3 \sin ^ { 2 } x + \sin x + 8 = 9 \cos ^ { 2 } x$$ giving your answers to 2 decimal places.
(b) Hence find the smallest positive solution of the equation $$3 \sin ^ { 2 } \left( 2 \theta - 30 ^ { \circ } \right) + \sin \left( 2 \theta - 30 ^ { \circ } \right) + 8 = 9 \cos ^ { 2 } \left( 2 \theta - 30 ^ { \circ } \right)$$ giving your answer to 2 decimal places.