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 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.
