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1.5 Trigonometry

1.5 Trigonometry

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Question 72

Let f(θ)=3cos⁡θ−6sin⁡θf(\theta) = 3\cos\theta - 6\sin\thetaf(θ)=3cosθ−6sinθ for θ∈R\theta \in \mathbb{R}θ∈R.

a.

Express f(θ)f(\theta)f(θ) in the form Rcos⁡(θ+α)R\cos(\theta + \alpha)Rcos(θ+α), where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of RRR and the value of α\alphaα, in radians, to 3 decimal places.

[3]
b.

The curve with equation y=cos⁡θy = \cos\thetay=cosθ is transformed onto the curve with equation y=f(θ)y = f(\theta)y=f(θ) by a sequence of two transformations.

Given that the first transformation is a stretch and the second is a translation:

(i) Describe fully the transformation that is a stretch. (ii) Describe fully the transformation that is a translation.

[4]
c.

Given g(θ)=755+(f(θ))2g(\theta) = \frac{75}{5 + (f(\theta))^2}g(θ)=5+(f(θ))275​, find the range of ggg.

[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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