A mechanical linkage tracks an angular displacement θ \theta\,θ radians. Its extension, EEE, is modelled by
E(θ)=−2cosec(θ+π)E(\theta) = -2\operatorname{cosec}(\theta + \pi)E(θ)=−2cosec(θ+π) for 0<θ<π 0 < \theta < \pi\,0<θ<π or π<θ<2π\pi < \theta < 2\piπ<θ<2π
Show that E(θ)=2cosecθE(\theta) = 2\operatorname{cosec}\thetaE(θ)=2cosecθ.
Sketch the graph of E E\,E against θ \theta\,θ for 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π, stating the equations of any vertical asymptotes and the coordinates of any local turning points.
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.