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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
