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1.5 Trigonometry

1.5 Trigonometry

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Question 141
a.

A laser tracking system uses a sensor where the angle xxx (in radians) of the beam relative to a horizontal axis must satisfy the equation:

5sec⁡2x+7tan⁡x=5 5\sec^2 x + 7\tan x = 5 5sec2x+7tanx=5

Determine all solutions for x x\,x in the interval −π<x≤0-\pi < x \le 0−π<x≤0, giving your answers to 3 significant figures where appropriate.

[5]
b.

In the study of resonance in a harmonic oscillator, an engineer encounters the following expression involving phase angles. Help them prove the identity:

sin⁡7βsin⁡2β−cos⁡7βcos⁡2β≡sin⁡5βsin⁡2βcos⁡2β \frac{\sin 7\beta}{\sin 2\beta} - \frac{\cos 7\beta}{\cos 2\beta} \equiv \frac{\sin 5\beta}{\sin 2\beta \cos 2\beta} sin2βsin7β​−cos2βcos7β​≡sin2βcos2βsin5β​
[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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