In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
A robotic arm's reach RRR (measured in cm) from a central hub is modeled by the equation
R(t)=3+2cost2+sint,0≤t≤2π R(t) = \frac{3 + 2 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi R(t)=2+sint3+2cost,0≤t≤2πwhere t t\,t is the time in seconds. A technician identifies a point in time M M\,M when the reach is at its absolute minimum.
Show that the value of t t\,t at M M\,M is a solution of the equation
4sint+3cost=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2Hence find, to 3 significant figures, the value of t t\,t at the point MMM.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, 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.
