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1.5 Trigonometry

1.5 Trigonometry

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Question 186

A robotic arm's vertical extension EEE (in cm) during a cycle is given by the function

E(t)=20sin⁡tcos⁡t−16sin⁡2t+11,t≥0 E(t) = 20 \sin t \cos t - 16 \sin^2 t + 11, \quad t \ge 0 E(t)=20sintcost−16sin2t+11,t≥0

where t t\,t is the time in seconds.

a.

Write E(t)E(t)E(t) in the form asin⁡2t+bcos⁡2t+ca \sin 2t + b \cos 2t + casin2t+bcos2t+c, where a,b, a, b,\,a,b, and c c\,c are integers to be determined.

[3]
b.

Use your result from part (a) to express E(t)E(t)E(t) in the form

Rsin⁡(2t+α)+c R \sin(2t + \alpha) + c Rsin(2t+α)+c

where R>0 R > 0\,R>0 and 0<α<π2\displaystyle 0 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of R R\,R and the value of α \alpha\,α in radians to 3 significant figures.

[3]
c.

Hence, or otherwise, (i) state the maximum extension of the robotic arm, (ii) find the second smallest positive value of t t\,t at which this maximum extension occurs, giving your answer to 3 significant figures.

[3]
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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