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1.7 Trigonometry

1.7 Trigonometry

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Question 93
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

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

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