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1.8 E: Trigonometry

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Question 146

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

16cos⁡β=5.2cosec⁡β 16 \cos \beta = 5.2 \operatorname{cosec} \beta 16cosβ=5.2cosecβ

where 0∘<β<90∘0^\circ < \beta < 90^\circ0∘<β<90∘.

a.

Show that this equation can be expressed in the form

sin⁡2β=k \sin 2\beta = k sin2β=k

where kkk is a constant to be determined.

[4]
b.

Hence determine the smallest positive value of β\betaβ, giving your answer in degrees to one decimal place.

[3]
Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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