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1.7 Trigonometry

1.7 Trigonometry

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Question 180

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​.

[4]
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

1.7 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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