Show that the equation
3cosϕ(tanϕsinϕ+1)=8cosϕ+13 \cos \phi ( \tan \phi \sin \phi + 1 ) = 8 \cos \phi + 13cosϕ(tanϕsinϕ+1)=8cosϕ+1
can be written in the form
3cos2ϕ+5cosϕ−2=03 \cos^2 \phi + 5 \cos \phi - 2 = 03cos2ϕ+5cosϕ−2=0
A mechanical sensor detects oscillations described by the phase equation
3cos3x(tan3xsin3x+1)=8cos3x+13 \cos 3x ( \tan 3x \sin 3x + 1 ) = 8 \cos 3x + 13cos3x(tan3xsin3x+1)=8cos3x+1
where x x\,x represents the angular position in degrees. Hence solve this equation for 0∘<x<180∘0^\circ < x < 180^\circ0∘<x<180∘, giving your answers to one decimal place.
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.