In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
In a study of harmonic oscillations, the phase angle ϕ\phiϕ (in degrees) of a combined wave satisfies the equation
3sin(ϕ+45∘)=2cos(ϕ−60∘) 3 \sin(\phi + 45^\circ) = 2 \cos(\phi - 60^\circ) 3sin(ϕ+45∘)=2cos(ϕ−60∘)Show that
tanϕ=2−33−6 \tan \phi = \frac{\sqrt{2} - 3}{3 - \sqrt{6}} tanϕ=3−62−3Hence or otherwise, solve, for 0∘≤θ<180∘0^\circ \le \theta < 180^\circ0∘≤θ<180∘,
3sin(3θ+45∘)=2cos(3θ−60∘) 3 \sin(3\theta + 45^\circ) = 2 \cos(3\theta - 60^\circ) 3sin(3θ+45∘)=2cos(3θ−60∘)giving your answers to one decimal place.
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.