A mechanical sensor measures the angular misalignment α \alpha\,α of a rotating component. The misalignment follows the equilibrium condition:
6sin(α−35∘)=−5cos(α−35∘) 6 \sin(\alpha - 35^\circ) = -5 \cos(\alpha - 35^\circ) 6sin(α−35∘)=−5cos(α−35∘)Determine all possible values of α \alpha\,α in the range 0<α<360∘0 < \alpha < 360^\circ0<α<360∘, giving your answers to one decimal place.
Show that the equation describing the lateral vibration of a specific piston,
5sin3x=7sinx−4sinxcosx 5 \sin^3 x = 7 \sin x - 4 \sin x \cos x 5sin3x=7sinx−4sinxcosxcan 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, b b\,b and c c\,c are integers to be found.
Hence find all real solutions for −π≤x≤π-\pi \le x \le \pi−π≤x≤π to the equation
5sin3x=7sinx−4sinxcosx 5 \sin^3 x = 7 \sin x - 4 \sin x \cos x 5sin3x=7sinx−4sinxcosxgiving 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.