A mechanical linkage is designed such that its angle of rotation, β\betaβ, in degrees, satisfies the equilibrium condition:
5tan(β−60∘)=2cos(β−60∘) 5 \tan(\beta - 60^\circ) = 2 \cos(\beta - 60^\circ) 5tan(β−60∘)=2cos(β−60∘)Find all possible values of β\betaβ in the interval −180∘<β≤180∘-180^\circ < \beta \le 180^\circ−180∘<β≤180∘. Give your answers to one decimal place where appropriate.
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.