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2015 RI P1 Q5

2015 RI P1 Q5

7 marks
Prelims

Without using a calculator,

  1. solve the inequality \(\frac{8-5x}{2x+1}\le 2-x\),[4]
  2. hence find the set of values of \(\theta \) for which \(\frac{8-5\sin \theta }{2\sin \theta +1}\le 2-\sin \theta \), where \(0<\theta <2\pi \).[3]

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Answer:(i) \(x < -\frac{1}{2}\) or \(\text{1}\le x\le 3\) (ii) \(\left\{ \theta \in \mathbb{R}:\frac{7}{6}\pi <\theta <\frac{11}{6}\pi ,\theta =\frac{\pi }{2} \right\}\)

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