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1.5 Trigonometry

1.5 Trigonometry

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Question 37

It is given that

(sin⁡θ+6cos⁡θ)2+(3sin⁡θ−2cos⁡θ)2=28(\sin\theta + 6\cos\theta)^2 + (3\sin\theta - 2\cos\theta)^2 = 28(sinθ+6cosθ)2+(3sinθ−2cosθ)2=28

and that θ \theta\,θ is obtuse.

a.

Find the exact value of sin⁡θ\sin\thetasinθ. Fully justify your answer.

[5]
b.

Find the exact value of cos⁡2θ\cos 2\thetacos2θ.

[1]
c.

Find the exact value of tan⁡θ\tan\thetatanθ, giving your answer in surd form.

[2]
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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