Solve, for 0<θ<360∘0 < \theta < 360^\circ0<θ<360∘, the equation
4sin(θ+40∘)=3cos(θ+40∘) 4 \sin(\theta + 40^\circ) = 3 \cos(\theta + 40^\circ) 4sin(θ+40∘)=3cos(θ+40∘)giving your answers to one decimal place.
Show that the equation
2sin3x=6sinx−5sinxcosx 2 \sin^3 x = 6 \sin x - 5 \sin x \cos x 2sin3x=6sinx−5sinxcosxcan be written in the form
sinx(acos2x+bcosx+c)=0 \sin x (a \cos^2 x + b \cos x + c) = 0 sinx(acos2x+bcosx+c)=0where aaa, bbb and ccc are constants to be found.
Hence solve for −π≤x≤π-\pi \le x \le \pi−π≤x≤π the equation
2sin3x=6sinx−5sinxcosx 2 \sin^3 x = 6 \sin x - 5 \sin x \cos x 2sin3x=6sinx−5sinxcosxgiving your answers to two decimal places where appropriate.
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.
