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1.5 Trigonometry

1.5 Trigonometry

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Question 184

The torque TTT (in N⋅\cdot⋅m) exerted on a specialized robotic hinge is modeled as a function of its rotation angle α\alphaα (in radians), where 0<α<2π0 < \alpha < 2\pi0<α<2π.

a.

Show that

cos⁡α(5tan⁡α+2tan⁡α)≡3sin⁡α+2sin⁡α \cos \alpha \left( 5 \tan \alpha + \frac{2}{\tan \alpha} \right) \equiv 3 \sin \alpha + \frac{2}{\sin \alpha} cosα(5tanα+tanα2​)≡3sinα+sinα2​

for α≠nπ2\alpha \neq \frac{n\pi}{2}α=2nπ​.

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b.

The hinge operates at a specific resistance where the torque is given by the relation T=9sin⁡α−2T = 9 \sin \alpha - 2T=9sinα−2. Hence determine, for 0<α<2π0 < \alpha < 2\pi0<α<2π, the possible values of α\alphaα such that

cos⁡α(5tan⁡α+2tan⁡α)=9sin⁡α−2 \cos \alpha \left( 5 \tan \alpha + \frac{2}{\tan \alpha} \right) = 9 \sin \alpha - 2 cosα(5tanα+tanα2​)=9sinα−2

giving your answers to 3 significant figures.

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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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