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1.5 Trigonometry

1.5 Trigonometry

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Question 208
a.

Show that 5cos⁡2t−5cos⁡6t≈80t25\cos 2t - 5\cos 6t \approx 80t^25cos2t−5cos6t≈80t2 for small values of ttt.

[3]
b.

The output signal of a high-frequency sensor is modeled by the function R(t)=120(5cos⁡2t−5cos⁡6t)R(t) = \sqrt{\frac{1}{20}(5\cos 2t - 5\cos 6t)}R(t)=201​(5cos2t−5cos6t)​. Show that for small positive values of ttt, the area enclosed by the curve y=R(t)y = R(t)y=R(t), the ttt-axis, and the line t=0.4t = 0.4t=0.4 can be approximated by Area≈2m×5n\text{Area} \approx 2^m \times 5^nArea≈2m×5n where mmm and nnn are integers to be found.

[3]
ci.

Explain why ∫12.612.72t dt\int_{12.6}^{12.7} 2t \, dt∫12.612.7​2tdt is not a suitable approximation for ∫12.612.7R(t) dt\int_{12.6}^{12.7} R(t) \, dt∫12.612.7​R(t)dt.

[1]
cii.

Explain how ∫12.612.7R(t) dt\int_{12.6}^{12.7} R(t) \, dt∫12.612.7​R(t)dt may be approximated by ∫ab2t dt\int_{a}^{b} 2t \, dt∫ab​2tdt for suitable values of aaa and bbb.

[2]
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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