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1.8 E: Trigonometry

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Question 104
a.

Express 5sin⁡x+12cos⁡x5\sin x + 12\cos x5sinx+12cosx in the form Rsin⁡(x+α)R\sin(x + \alpha)Rsin(x+α), where R>0 R > 0\,R>0 and 0°≤α≤90°0° \leq \alpha \leq 90°0°≤α≤90°. Give α \alpha\,α to one decimal place.

[4]
b.

Hence find the maximum value of 5sin⁡x+12cos⁡x5\sin x + 12\cos x5sinx+12cosx, and the smallest positive value of x x\,x at which this maximum occurs.

[3]
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.

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