In the study of oscillatory motion, the angular displacement of a mechanical sensor is determined to be zero when the tilt angle β\betaβ satisfies the equation 16cosβ=5.2cosecβ16 \cos \beta = 5.2 \operatorname{cosec} \beta16cosβ=5.2cosecβ where 0∘<β<90∘0^\circ < \beta < 90^\circ0∘<β<90∘.
Show that this equation can be expressed in the form sin2β=k\sin 2\beta = ksin2β=k where kkk is a constant to be determined.
Hence determine the smallest positive value of β\betaβ, giving your answer in degrees to one decimal place.
Practise Edexcel A Level Maths 7.2 Double Angle Formulae with exam-style questions for A Level Maths. 24 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.