Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The required equation is $\cot x = 2 - \cos x$.
(a)[2]
By drawing suitable graphs, show that the equation $\cot x = 2 - \cos x$ has one root in the interval $0 < x \leq \frac{1}{2}\pi$.
(b)[2]
Show by calculation that this root lies between $0.6$ and $0.8$.
(c)[3]
Use the iterative formula $x_{n+1} = \tan^{-1}\!\left(\frac{1}{2-\cos x_n}\right)$ to find the root correct to $2$ decimal places. Give each iteration result to $4$ decimal places.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Draw a suitable graph, for example $y=\cot x$, with the correct intercept and curvature.” …