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1.8 E: Trigonometry

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Question 184

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]

1.8 E: Trigonometry Questions

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

Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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