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Numerical Methods

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Question 48

The diagram shows a sector of a circle AOBAOBAOB. Angle AOB AOB\,AOB is θ \theta\,θ radians.

A sector diagram with horizontal chord AB, centre O below it, radii OA and OB, an upper circular arc, and central angle θ.

Given that the area of triangle AOB AOB\,AOB is 12\displaystyle \frac{1}{2}21​ the area of sector AOBAOBAOB.

a.

Show that sin⁡θ−12θ=0\displaystyle \sin \theta - \frac{1}{2} \theta = 0sinθ−21​θ=0

[3]
b.

Use the Newton-Raphson method with θ0=2\theta_0 = 2θ0​=2, to find θ4 \theta_4\,θ4​ as an approximation for θ\thetaθ. Give your answer to be 4 decimal places.

[3]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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