Determine the phase angles ϕ\phiϕ, in the range −60∘<ϕ<60∘-60^\circ < \phi < 60^\circ−60∘<ϕ<60∘, that satisfy the following equilibrium condition for a mechanical oscillator:
5sin(3ϕ+10∘)+2cos(3ϕ+10∘)=0 5 \sin(3\phi + 10^\circ) + 2 \cos(3\phi + 10^\circ) = 0 5sin(3ϕ+10∘)+2cos(3ϕ+10∘)=0giving your answers to one decimal place.
A periodic voltage signal V V\,V follows the model
5sin2t−8cost=2 5 \sin^2 t - 8 \cos t = 2 5sin2t−8cost=2Find all values of t t\,t in the range 0<t<2π 0 < t < 2\pi\,0<t<2π for which this model holds, giving your answers to 3 significant figures.
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.
