In a stability analysis for a rotating pendulum, the equilibrium angle α\alphaα in the interval 0<α≤π0 < \alpha \le \pi0<α≤π satisfies the equation
2cosec2α−5cotα=5 2\text{cosec}^2 \alpha - 5\cot \alpha = 5 2cosec2α−5cotα=5Determine all possible values for α\alphaα, giving your answers to 3 significant figures.
Prove the following trigonometric identity for all valid values of θ\thetaθ:
sin8θsin3θ−cos8θcos3θ≡sin5θsin3θcos3θ \frac{\sin 8\theta}{\sin 3\theta} - \frac{\cos 8\theta}{\cos 3\theta} \equiv \frac{\sin 5\theta}{\sin 3\theta \cos 3\theta} sin3θsin8θ−cos3θcos8θ≡sin3θcos3θsin5θPractise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) 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.
