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.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.