The horizontal position x x\,x of a piston in a high-precision engine is modelled by the equation
x=18cos2(2θ)0<θ<π4x = 18 \cos^2(2\theta) \qquad 0 < \theta < \frac{\pi}{4}x=18cos2(2θ)0<θ<4π
where θ \theta\,θ is the crankshaft angle in radians.
Show that the rate of change of the angle with respect to the position, dθdx\displaystyle \frac{d\theta}{dx}dxdθ, can be expressed in the form
dθdx=−1ABx−x2\frac{d\theta}{dx} = -\frac{1}{A\sqrt{Bx - x^2}}dxdθ=−ABx−x21
where A A\,A and B B\,B are integers to be determined.
Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 questions, 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.