A precision laser-cutting head moves along a path C C\,C in a vertical plane. Its horizontal displacement sss (cm) and vertical height hhh (cm) are modelled by the parametric equations
s=5+3sinθ s = 5 + 3 \sin \theta s=5+3sinθ h=167+cos2θ h = \frac{16}{7 + \cos 2\theta} h=7+cos2θ16for −π2≤θ≤π2-\frac{\pi}{2} \le \theta \le \frac{\pi}{2}−2π≤θ≤2π.
Show that the path C C\,C has the Cartesian equation
h=72(11−s)(s+1)p≤s≤q h = \frac{72}{(11 - s)(s + 1)} \quad p \le s \le q h=(11−s)(s+1)72p≤s≤qwhere p p\,p and q q\,q are constants to be found.
Hence, find a Cartesian equation for C C\,C in the form
h=as+b+cs+dp≤s≤q h = \frac{a}{s + b} + \frac{c}{s + d} \quad p \le s \le q h=s+ba+s+dcp≤s≤qwhere a,b,c a, b, c\,a,b,c and d d\,d are constants.
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, 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.
