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1.5 Trigonometry

1.5 Trigonometry

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Question 1
a.

Show that

cos⁡θ(9tan⁡θ+4tan⁡θ)≡5sin⁡θ+4sin⁡θ \cos \theta \left( 9 \tan \theta + \frac{4}{\tan \theta} \right) \equiv 5 \sin \theta + \frac{4}{\sin \theta} cosθ(9tanθ+tanθ4​)≡5sinθ+sinθ4​

for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ​, where nnn is an integer.

[3]
b.

Hence solve, for 0<x<2π0 < x < 2\pi0<x<2π, the equation

cos⁡x(9tan⁡x+4tan⁡x)=12sin⁡x−2 \cos x \left( 9 \tan x + \frac{4}{\tan x} \right) = 12 \sin x - 2 cosx(9tanx+tanx4​)=12sinx−2

giving your answers to 3 significant figures.

[5]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

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