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=5.2cosecβ 16 \cos \beta = 5.2 \operatorname{cosec} \beta 16cosβ=5.2cosecβwhere 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 = k sin2β=kwhere 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 AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) 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.
