The vertical displacement HHH, in millimetres, of a high-precision camera sensor at time t t\,t seconds is modeled by the function:
H(t)=sect+5t−7,0<t<π2H(t) = \sec t + 5t - 7, \quad 0 < t < \frac{\pi}{2}H(t)=sect+5t−7,0<t<2π
A calibration reset is triggered when the displacement is zero, at time t=αt = \alphat=α.
Show that 1.0<α<1.11.0 < \alpha < 1.11.0<α<1.1.
Show that α \alpha\,α is a solution of the equation
t=75−15costt = \frac{7}{5} - \frac{1}{5\cos t}t=57−5cost1
The iterative formula
tn+1=75−15costnt_{n+1} = \frac{7}{5} - \frac{1}{5\cos t_n}tn+1=57−5costn1
is used to approximate the value of α\alphaα.
Starting with t1=1.05t_1 = 1.05t1=1.05 and using the iterative formula: (i) find, to 4 decimal places, the value of t2t_2t2. (ii) find, to 4 decimal places, the value of α\alphaα.
Practise Edexcel A Level Maths 10.2 Iteration with exam-style questions for A Level Maths. 32 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.