The orientation angle ϕ \phi\,ϕ of a precision solar tracker satisfies the equation
5sin(ϕ−60∘)+12cos(ϕ−60∘)=0 5 \sin(\phi - 60^\circ) + 12 \cos(\phi - 60^\circ) = 0 5sin(ϕ−60∘)+12cos(ϕ−60∘)=0Determine 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−7sinαcosα 3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha 3sin3α=10sinα−7sinαcosαcan be expressed in the form
sinα(kcos2α+mcosα+n)=0 \sin \alpha (k \cos^2 \alpha + m \cos \alpha + n) = 0 sinα(kcos2α+mcosα+n)=0where 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−7sinαcosα 3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha 3sin3α=10sinα−7sinαcosαfor −π≤α≤π-\pi \le \alpha \le \pi−π≤α≤π.
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.
