In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The depth of water in a storage tank, H H\,H metres, at time t t\,t hours after midnight is modelled by the equation
H=6+4cost2+sint,0≤t≤2πH = \frac{6 + 4 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\piH=2+sint6+4cost,0≤t≤2π
The point M M\,M on the curve represents the time at which the water depth reaches its local minimum.
Show that the ttt-coordinate of M M\,M is a solution of the equation 4sint+3cost=−24 \sin t + 3 \cos t = -24sint+3cost=−2
Hence find, to 3 significant figures, the ttt-coordinate of MMM.
Practise Edexcel A Level Maths 9.5 The Quotient Rule with exam-style questions for A Level Maths. 29 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.