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1.5 Trigonometry

1.5 Trigonometry

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Question 3
54%
a.

Use the identity cos⁡2θ+sin⁡2θ=1\cos^2\theta + \sin^2\theta = 1cos2θ+sin2θ=1 to prove that tan⁡2θ=sec⁡2θ−1\tan^2\theta = \sec^2\theta - 1tan2θ=sec2θ−1

[2]
b.

Solve, for 0≤θ≤3600 \leq \theta \leq 3600≤θ≤360, the equation,

tan⁡2θ+sec⁡2θ+5sec⁡θ=2 \tan^2\theta + \sec^2\theta + 5\sec\theta = 2 tan2θ+sec2θ+5secθ=2

Give your answers to 1 decimal place.

[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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