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.
317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.