The orientation angle ϕ \phi\,ϕ of a precision solar tracker satisfies the equation 5sin(ϕ−60∘)+12cos(ϕ−60∘)=05 \sin(\phi - 60^\circ) + 12 \cos(\phi - 60^\circ) = 05sin(ϕ−60∘)+12cos(ϕ−60∘)=0 Determine all possible values of ϕ \phi\,ϕ in the range 0∘<ϕ<360∘0^\circ < \phi < 360^\circ0∘<ϕ<360∘, giving your answers to one decimal place.
Show that the equation 3sin3α=10sinα−7sinαcosα3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha3sin3α=10sinα−7sinαcosα can be expressed in the form sinα(kcos2α+mcosα+n)=0\sin \alpha (k \cos^2 \alpha + m \cos \alpha + n) = 0sinα(kcos2α+mcosα+n)=0 where k,m k, m\,k,m and n n\,n are constants to be determined.
Hence find the exact solutions of the equation 3sin3α=10sinα−7sinαcosα3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha3sin3α=10sinα−7sinαcosα for −π≤α≤π-\pi \le \alpha \le \pi−π≤α≤π.
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.