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≈Awhere A A\,A is a constant to be determined.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.