Edexcel C4 2010 January — Question 3

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2010
SessionJanuary
TopicImplicit equations and differentiation

  1. The curve \(C\) has the equation
$$\cos 2 x + \cos 3 y = 1 , \quad - \frac { \pi } { 4 } \leqslant x \leqslant \frac { \pi } { 4 } , \quad 0 \leqslant y \leqslant \frac { \pi } { 6 }$$
  1. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\). The point \(P\) lies on \(C\) where \(x = \frac { \pi } { 6 }\).
  2. Find the value of \(y\) at \(P\).
  3. Find the equation of the tangent to \(C\) at \(P\), giving your answer in the form \(a x + b y + c \pi = 0\), where \(a , b\) and \(c\) are integers. \section*{LU}