Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
A semicircle has centre $O$, radius $r$ and diameter $AB$ as shown. The point $P$ on the circumference is positioned so that the area of the minor segment on $AP$ is equal to half the area of the minor segment on $BP$. The angle $AOP$ is $x$ radians.
(i)[3]
Show that $x$ is a solution of the equation $x = \frac{1}{3}(\pi + \sin x)$.
(ii)[2]
Confirm by calculation that $x$ is between $1$ and $1.5$.
(iii)[3]
Use the iterative formula derived from the equation in part (i) to find $x$ correct to $3$ decimal places. Give every iterative value to $5$ decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct sector formula at least once and set up an equation in $r$ and $x$” …