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1.8 E: Trigonometry

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Question 118
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]

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