Figure 1 below shows the sector AOB AOB\,AOB of a circle. The angle AOB AOB\,AOB is θ \theta\,θ radians.
The area of the triangle AOB AOB\,AOB is 34\displaystyle \frac{3}{4}43 of the area of the sector AOBAOBAOB.
Show that sinθ−34θ=0\displaystyle \sin\theta - \frac{3}{4}\theta = 0sinθ−43θ=0.
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 four decimal places, and show the result of each iteration.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.