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≤2π H = \frac{6 + 4 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi H=2+sint6+4cost,0≤t≤2πThe 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=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2Hence find, to 3 significant figures, the ttt-coordinate of MMM.
