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≈AF \approx AF≈A
where A A\,A is a constant to be determined.
Practise Edexcel A Level Maths Radians with exam-style questions for A Level Maths. 52 questions covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.