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.
137 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.