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Trigonometry and Modelling

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Question 11
a.

Express sin⁡x−3cos⁡x\sin x - 3 \cos xsinx−3cosx in the form Rsin⁡(x−α)R \sin (x - \alpha)Rsin(x−α), where R=10R = \sqrt{10}R=10​ and 0≤α≤π2\displaystyle 0 \leq \alpha \leq \frac{\pi}{2}0≤α≤2π​

[3]
b.

Hence find the greatest value of (sin⁡x−3cos⁡x)2(\sin x - 3 \cos x)^2(sinx−3cosx)2 and find, the smallest positive value of x x\,x for which this maximum occurs

[2]
c.

Solve, for 0≤x≤2π0 \leq x \leq 2\pi0≤x≤2π,

sin⁡x−3cos⁡x=1 \sin x - 3 \cos x = 1 sinx−3cosx=1

Give your answers to 3 decimal places.

[5]
Markscheme

Trigonometry and Modelling Questions

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

348 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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