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1.8 E: Trigonometry

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Question 151
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]

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.

Question bank