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Trigonometry and Modelling

Trigonometry and Modelling

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Question 96
a.

Show that

cos⁡2xsin⁡x+sin⁡2xcos⁡x≡csc⁡x,x≠nπ2,  n∈Z \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \equiv \csc x, \quad x \neq \frac{n\pi}{2}, \; n \in \mathbb{Z} sinxcos2x​+cosxsin2x​≡cscx,x=2nπ​,n∈Z
[3]
b.

In a study of fluid dynamics, the pressure coefficient PPP is modeled by the equation

(cos⁡2θsin⁡θ+sin⁡2θcos⁡θ)2=7−cot⁡θ \left( \frac{\cos 2\theta}{\sin \theta} + \frac{\sin 2\theta}{\cos \theta} \right)^2 = 7 - \cot \theta (sinθcos2θ​+cosθsin2θ​)2=7−cotθ

Hence solve this equation for 0<θ<π0 < \theta < \pi0<θ<π, giving your answers to 3 significant figures as appropriate.

[5]
c.

Using the result from part (a), or otherwise, find the exact value of

∫π6π4(cos⁡2xsin⁡x+sin⁡2xcos⁡x)cot⁡x dx \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \left( \frac{\cos 2x}{\sin x} + \frac{\sin 2x}{\cos x} \right) \cot x \, dx ∫6π​4π​​(sinxcos2x​+cosxsin2x​)cotxdx
[3]
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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