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=3−62−3
Hence 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.
Practise Edexcel A Level Maths 7.1 Addition Formulae with exam-style questions for A Level Maths. 3 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.