The angular displacement α\alphaα (in degrees) of a robotic sensor arm during a precision sweep is governed by the relation:
−6cosα(tanαsinα−1)=7cosα−4 -6 \cos \alpha ( \tan \alpha \sin \alpha - 1 ) = 7 \cos \alpha - 4 −6cosα(tanαsinα−1)=7cosα−4Show that this relation can be simplified to the quadratic form:
6cos2α−cosα−2=0 6 \cos^2 \alpha - \cos \alpha - 2 = 0 6cos2α−cosα−2=0During a secondary calibration cycle, the arm operates such that the input angle is 3ϕ3\phi3ϕ. Find all values of ϕ \phi\,ϕ in the interval 0≤ϕ≤180∘ 0 \le \phi \le 180^\circ\,0≤ϕ≤180∘ such that:
−6cos3ϕ(tan3ϕsin3ϕ−1)=7cos3ϕ−4 -6 \cos 3\phi ( \tan 3\phi \sin 3\phi - 1 ) = 7 \cos 3\phi - 4 −6cos3ϕ(tan3ϕsin3ϕ−1)=7cos3ϕ−4giving your answers to one decimal place where appropriate.
Practise 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.
