A curve, CCC, has the equation 5siny+xcosy=Ax5 \sin y + x \cos y = Ax5siny+xcosy=Ax where A A\,A is a constant. C C\,C passes through the point P(3,π3)\displaystyle P \left( \sqrt{3}, \frac{\pi}{3} \right)P(3,3π)
Using the fact that C C\,C passes through P P\,P and differentiating the equation of CCC, show that A=3A = 3A=3 and dydx=3−cosy5cosy−xsiny\displaystyle \frac{dy}{dx} = \frac{3 - \cos y}{5 \cos y - x \sin y}dxdy=5cosy−xsiny3−cosy
Hence find the equation of the tangent to C C\,C at PPP.
717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.