(i)[3]
Show that $x$ satisfies the equation $\tan x = x + \pi$.
(ii)[3]
Apply the iterative formula $x_{n+1} = \tan^{-1}(x_n + \pi)$ to find $x$ correct to 2 decimal places. Write each iterate to 4 decimal places.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The figure presents a semicircle $ACB$ with centre $O$ and radius $r$. The tangent drawn at $C$ intersects $AB$ extended at $T$. The angle $BOC$ is $x$ radians. The shaded area is the same as the area of the semicircle.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write down, or make clear, $CT = r \tan x$ or $OT = r \sec x$, or an equivalent relation” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI