OCR C3 2010 January — Question 2

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2010
SessionJanuary
TopicAddition & Double Angle Formulae

2 The angle \(\theta\) is such that \(0 ^ { \circ } < \theta < 90 ^ { \circ }\).
  1. Given that \(\theta\) satisfies the equation \(6 \sin 2 \theta = 5 \cos \theta\), find the exact value of \(\sin \theta\).
  2. Given instead that \(\theta\) satisfies the equation \(8 \cos \theta \operatorname { cosec } ^ { 2 } \theta = 3\), find the exact value of \(\cos \theta\).