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1.5 Trigonometry

1.5 Trigonometry

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Question 175
a.

Express 8sin⁡x−15cos⁡x8 \sin x - 15 \cos x8sinx−15cosx in the form Rsin⁡(x−α)R \sin(x - \alpha)Rsin(x−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 function ggg is defined by

g(θ)=15+8sin⁡(3θ−π4)−15cos⁡(3θ−π4),θ>0 g(\theta) = 15 + 8 \sin\left(3\theta - \frac{\pi}{4}\right) - 15 \cos\left(3\theta - \frac{\pi}{4}\right), \quad \theta > 0 g(θ)=15+8sin(3θ−4π​)−15cos(3θ−4π​),θ>0

Find (i) the minimum value of g(θ)g(\theta)g(θ) (ii) the smallest value of θ\thetaθ at which this minimum value occurs.

[3]
c.

The function hhh is defined by

h(β)=5−(8sin⁡β−15cos⁡β)2 h(\beta) = 5 - (8 \sin \beta - 15 \cos \beta)^2 h(β)=5−(8sinβ−15cosβ)2

Find the range of hhh.

[4]
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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