The movement of a precision robotic arm across a flat surface is defined by the parametric relationship
x=6cos2y0≤x≤6,0≤y≤π4 x = 6 \cos 2y \quad 0 \le x \le 6, \quad 0 \le y \le \frac{\pi}{4} x=6cos2y0≤x≤6,0≤y≤4πwhere xxx is the horizontal position in millimetres and yyy is the control angle in radians.
Find dxdy\frac{dx}{dy}dydx in terms of yyy.
Hence show that
dydx=k36−x2 \frac{dy}{dx} = \frac{k}{\sqrt{36-x^2}} dxdy=36−x2kwhere kkk is a constant to be found.
A specific calibration point P(a,b)P(a, b)P(a,b) lies on the path of the arm. Given that
find the exact values of aaa and bbb.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
