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1.8 E: Trigonometry

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Question 4
a.

Show that, for small values of θ \theta\,θ measured in radians,

2cos⁡3θ+sin⁡4θ−tan⁡θ≈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.

[3]
b.

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

2cos⁡0.21+sin⁡0.28−tan⁡0.072\cos 0.21 + \sin 0.28 - \tan 0.072cos0.21+sin0.28−tan0.07

Give your answer to three decimal places.

[2]
c.

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.

[2]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank