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1.7 Trigonometry

1.7 Trigonometry

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Question 181

The deflection DDD of a micro-cantilever, in micrometres, is modelled for small tilt angles θ\thetaθ (measured in radians) by the expression

D=2cos⁡4θ+3sin⁡2θ−tan⁡5θ D = 2 \cos 4\theta + 3 \sin 2\theta - \tan 5\theta D=2cos4θ+3sin2θ−tan5θ
a.

Show that, for small values of θ\thetaθ, the deflection can be approximated by the quadratic form

P+Qθ+Rθ2 P + Q\theta + R\theta^2 P+Qθ+Rθ2

where PPP, QQQ and RRR are constants to be found.

[4]
b.

Use your answer to part (a) to find an approximation for the deflection when

2cos⁡0.16+3sin⁡0.08−tan⁡0.20 2 \cos 0.16 + 3 \sin 0.08 - \tan 0.20 2cos0.16+3sin0.08−tan0.20

Give your answer to three decimal places.

[3]
Markscheme

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

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.

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