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1.8 E: Trigonometry

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Question 70

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.

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Markscheme

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context. Each one has a worked solution and a mark scheme showing where the marks go.

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