OCR C2 2016 June — Question 9

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2016
SessionJune
TopicTrig Graphs & Exact Values

9 A curve has equation \(y = \sin ( a x )\), where \(a\) is a positive constant and \(x\) is in radians.
  1. State the period of \(y = \sin ( a x )\), giving your answer in an exact form in terms of \(a\).
  2. Given that \(x = \frac { 1 } { 5 } \pi\) and \(x = \frac { 2 } { 5 } \pi\) are the two smallest positive solutions of \(\sin ( a x ) = k\), where \(k\) is a positive constant, find the values of \(a\) and \(k\).
  3. Given instead that \(\sin ( a x ) = \sqrt { 3 } \cos ( a x )\), find the two smallest positive solutions for \(x\), giving your answers in an exact form in terms of \(a\). \section*{END OF QUESTION PAPER}