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1.5 Trigonometry

1.5 Trigonometry

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Question 122

A sub-aquatic drone's descent angle θ \theta\,θ is controlled by a buoyancy system. To maintain stable movement, the angle must satisfy the equilibrium equation:

5cot⁡2θ+3 cosec2θ=2 cosec θ+10 5\cot^2\theta + 3\text{ cosec}^2\theta = 2\text{ cosec }\theta + 10 5cot2θ+3 cosec2θ=2 cosec θ+10
a.

Show that this equation can be written in the form

a cosec2θ+b cosec θ+c=0 a\text{ cosec}^2\theta + b\text{ cosec }\theta + c = 0 a cosec2θ+b cosec θ+c=0

where aaa, bbb, and c c\,c are integers to be found.

[3]
b.

Hence, given that the drone is tilted at an obtuse angle θ \theta\,θ that satisfies this stability equation, determine the exact value of tan⁡θ\tan \thetatanθ. Fully justify your answer.

[4]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

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