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Trigonometry and Modelling

Trigonometry and Modelling

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Question 67
a.

Show that the equation

3cos⁡ϕ(tan⁡ϕsin⁡ϕ+1)=8cos⁡ϕ+1 3 \cos \phi ( \tan \phi \sin \phi + 1 ) = 8 \cos \phi + 1 3cosϕ(tanϕsinϕ+1)=8cosϕ+1

can be written in the form

3cos⁡2ϕ+5cos⁡ϕ−2=0 3 \cos^2 \phi + 5 \cos \phi - 2 = 0 3cos2ϕ+5cosϕ−2=0
[3]
b.

A mechanical sensor detects oscillations described by the phase equation

3cos⁡3x(tan⁡3xsin⁡3x+1)=8cos⁡3x+1 3 \cos 3x ( \tan 3x \sin 3x + 1 ) = 8 \cos 3x + 1 3cos3x(tan3xsin3x+1)=8cos3x+1

where x x\,x represents the angular position in degrees. Hence solve this equation for 0∘<x<180∘0^\circ < x < 180^\circ0∘<x<180∘, giving your answers to one decimal place.

[4]
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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