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<2π0 < \theta < 2\pi0<θ<2π, θ≠π\theta \neq \piθ=π
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 < \theta < 2\pi0<θ<2π, stating the equations of any vertical asymptotes and the coordinates of any local turning points.
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.