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1.5 Trigonometry

1.5 Trigonometry

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Question 123
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

1.5 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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