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 \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 (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.