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1.7 Trigonometry

1.7 Trigonometry

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Question 182

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

1.7 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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