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 AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.