Show that, for small values of θ \theta\,θ measured in radians,
2cos3θ+sin4θ−tanθ≈A+Bθ+Cθ22\cos 3\theta + \sin 4\theta - \tan\theta \approx A + B\theta + C\theta^22cos3θ+sin4θ−tanθ≈A+Bθ+Cθ2
where AAA, B B\,B and C C\,C are constants to be found.
Use your answer to part (a) to find an approximation for
2cos0.21+sin0.28−tan0.072\cos 0.21 + \sin 0.28 - \tan 0.072cos0.21+sin0.28−tan0.07
Give your answer to three decimal places.
The true value of the expression in part (b) is 2.1623 to four decimal places. Calculate the percentage error in your approximation, giving your answer to two significant figures.
225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.