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3.4 Trigonometry (A-level only)

3.4 Trigonometry (A-level only)

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Question 104
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

3.4 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.4 Trigonometry (A-level only)

221 exam-style questions on CCEA A Level Maths 3.4 Trigonometry (A-level only), covering 3.4.1 Trigonometry (A-level only), 3.4.2 Trigonometry (A-level only), 3.4.3 Trigonometry (A-level only), 3.4.4 Trigonometry (A-level only), 3.4.5 Trigonometry (A-level only), 3.4.6 Trigonometry (A-level only), 3.4.7 Trigonometry (A-level only), and 3.4.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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