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1.5 Trigonometry

1.5 Trigonometry

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Question 81

The efficiency E E\,E of a precision-engineered joint in a robotic limb is determined by the tilt angle ϕ \phi\,ϕ such that

(sin⁡ϕ+12cos⁡ϕ)2+(4sin⁡ϕ−3cos⁡ϕ)2=119 (\sin \phi + 12 \cos \phi)^2 + (4 \sin \phi - 3 \cos \phi)^2 = 119 (sinϕ+12cosϕ)2+(4sinϕ−3cosϕ)2=119

Given that the joint is positioned at an obtuse angle, such that π2<ϕ<π\displaystyle \frac{\pi}{2} < \phi < \pi2π​<ϕ<π, determine the exact value of sin⁡ϕ\sin \phisinϕ. Fully justify your answer.

[6]
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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