Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram represents a circle centred at $O$ with radius $r$. The minor sector $AOB$ has angle $x$ radians. The area of the major sector is 3 times the area of the shaded region.
(a)[4]
Show that $x$ satisfies $x = \frac{3}{4}\sin x + \frac{1}{2}\pi$.
(b)[2]
Show by calculation that the solution to the equation in (a) lies between $2$ and $2.5$.
(c)[3]
Use the iterative formula derived from the equation in (a) to find this root correct to $2$ decimal places, and write each iterate to $4$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or otherwise indicate that the area of the major sector is $\frac12 r^2(2\pi-x)$.” …