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1.8 E: Trigonometry

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Question 51

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

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank