A polarizing lens reduces the intensity of an incoming light beam according to the model
L(θ)=12cos2θ L(\theta) = 12\cos^2 \theta L(θ)=12cos2θwhere LLL is the transmitted intensity in candelas and θ\thetaθ is the orientation angle of the lens in radians.
Determine all values of θ\thetaθ in the interval 0≤θ≤2π0 \le \theta \le 2\pi0≤θ≤2π for which the transmitted intensity is exactly 999 candelas. Give your answers as exact multiples of π\piπ.
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.