In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Two acoustic waves are superimposed such that their resulting phase angle ϕ\phiϕ satisfies the equation 6sin(ϕ−60∘)=2cos(ϕ+45∘)\sqrt{6} \sin(\phi - 60^\circ) = 2 \cos(\phi + 45^\circ)6sin(ϕ−60∘)=2cos(ϕ+45∘)
Show that tanϕ=52+3\tan \phi = \frac{5}{2 + \sqrt{3}}tanϕ=2+35 and hence that tanϕ=10−53\tan \phi = 10 - 5\sqrt{3}tanϕ=10−53
Hence or otherwise, solve for 0≤θ<180∘0 \le \theta < 180^\circ0≤θ<180∘, 6sin(3θ−60∘)=2cos(3θ+45∘)\sqrt{6} \sin(3\theta - 60^\circ) = 2 \cos(3\theta + 45^\circ)6sin(3θ−60∘)=2cos(3θ+45∘) giving your answers to one decimal place.
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions 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, 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.