Show that, for small values of θ\thetaθ measured in radians,
3cos2θ+sin4θ−2tan3θ≈A+Bθ+Cθ2 3 \cos 2\theta + \sin 4\theta - 2 \tan 3\theta \approx A + B\theta + C\theta^2 3cos2θ+sin4θ−2tan3θ≈A+Bθ+Cθ2where AAA, BBB and CCC are constants to be found.
Use your answer to part (a) to find an approximation for
3cos0.12+sin0.24−2tan0.18 3 \cos 0.12 + \sin 0.24 - 2 \tan 0.18 3cos0.12+sin0.24−2tan0.18Give your answer to three decimal places.
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.