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−4
Show that this relation can be simplified to the quadratic form:
6cos2α−cosα−2=06 \cos^2 \alpha - \cos \alpha - 2 = 06cos2α−cosα−2=0
During 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−4
giving your answers to one decimal place where appropriate.
Practise Edexcel A Level Maths 7.3 Solving Trigonometric Equations with exam-style questions for A Level Maths. 29 questions, 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.