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1.8 E: Trigonometry

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Question 25

An optical sensor measures the flux F F\,F of light entering an aperture at a small angle ϕ \phi\,ϕ radians. The flux is modelled by the expression:

F=1−cos⁡(14ϕ)ϕsin⁡(7ϕ) F = \frac{1 - \cos(14\phi)}{\phi \sin(7\phi)} F=ϕsin(7ϕ)1−cos(14ϕ)​

Using small angle approximations, show that for small, non-zero values of ϕ\phiϕ,

F≈A F \approx A F≈A

where A A\,A is a constant to be determined.

[4]
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.

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