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1.7 Trigonometry

1.7 Trigonometry

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Question 148

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

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

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