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Trigonometry and Modelling

Trigonometry and Modelling

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Question 12
a.

Show that the equation

[6sin⁡θcos⁡θcos⁡θ+sin⁡θ=(4+2sec⁡2θ)(cos⁡θ−sin⁡θ) [\frac{6 \sin \theta \cos \theta}{\cos \theta + \sin \theta} = (4 + 2\sec 2\theta)(\cos \theta - \sin \theta) [cosθ+sinθ6sinθcosθ​=(4+2sec2θ)(cosθ−sinθ)

can be written in the form

3sin⁡2θ−4cos⁡2θ=2 3 \sin 2\theta - 4 \cos 2\theta = 2 3sin2θ−4cos2θ=2
[5]
b.

Hence solve for 0<x<π0 < x < \pi0<x<π

[6sin⁡xcos⁡xcos⁡x+sin⁡x=(4+2sec⁡2x)(cos⁡x−sin⁡x) [\frac{6 \sin x \cos x}{\cos x + \sin x} = (4 + 2\sec 2x)(\cos x - \sin x) [cosx+sinx6sinxcosx​=(4+2sec2x)(cosx−sinx)

giving your answers to 3 significant figures.

[5]
Markscheme

Trigonometry and Modelling Questions

  1. A Level
  2. /Maths
  3. /Trigonometry and Modelling

137 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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