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1.5 Trigonometry

1.5 Trigonometry

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Question 92

The angular displacement, ϕ\phiϕ, of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:

11sec⁡ϕ=32sin⁡ϕ 11 \sec \phi = 32 \sin \phi 11secϕ=32sinϕ
a.

Show that this equation can be expressed in the form sin⁡2ϕ=k\sin 2\phi = ksin2ϕ=k, where k k\,k is a constant to be determined.

[4]
b.

Hence, find the smallest positive value of ϕ\phiϕ, in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.

[3]
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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