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1.5 Trigonometry

1.5 Trigonometry

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Question 153

The angular displacement α\alphaα (in degrees) of a robotic sensor arm during a precision sweep is governed by the relation:

−6cos⁡α(tan⁡αsin⁡α−1)=7cos⁡α−4 -6 \cos \alpha ( \tan \alpha \sin \alpha - 1 ) = 7 \cos \alpha - 4 −6cosα(tanαsinα−1)=7cosα−4
a.

Show that this relation can be simplified to the quadratic form:

6cos⁡2α−cos⁡α−2=0 6 \cos^2 \alpha - \cos \alpha - 2 = 0 6cos2α−cosα−2=0
[3]
b.

During a secondary calibration cycle, the arm operates such that the input angle is 3ϕ3\phi3ϕ. Find all values of ϕ \phi\,ϕ in the interval 0≤ϕ≤180∘ 0 \le \phi \le 180^\circ\,0≤ϕ≤180∘ such that:

−6cos⁡3ϕ(tan⁡3ϕsin⁡3ϕ−1)=7cos⁡3ϕ−4 -6 \cos 3\phi ( \tan 3\phi \sin 3\phi - 1 ) = 7 \cos 3\phi - 4 −6cos3ϕ(tan3ϕsin3ϕ−1)=7cos3ϕ−4

giving your answers to one decimal place where appropriate.

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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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