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.
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions, matched to the Edexcel A Level Maths (9MA0) 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.