Edexcel C3 2007 January — Question 3

Exam BoardEdexcel
ModuleC3 (Core Mathematics 3)
Year2007
SessionJanuary
TopicImplicit equations and differentiation

3. The curve \(C\) has equation $$x = 2 \sin y .$$
  1. Show that the point \(P \left( \sqrt { } 2 , \frac { \pi } { 4 } \right)\) lies on \(C\).
  2. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { \sqrt { 2 } }\) at \(P\).
  3. Find an equation of the normal to \(C\) at \(P\). Give your answer in the form \(y = m x + c\), where \(m\) and \(c\) are exact constants.