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1.5 Trigonometry

1.5 Trigonometry

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Question 31

In an investigation of harmonic motion, a physicist requires the double-angle identities for an angle θ\thetaθ.

a.

Starting with the identity for sin⁡(A+B)\sin(A + B)sin(A+B), find an expression for sin⁡2θ \sin 2\theta\,sin2θ in terms of sin⁡θ \sin \theta\,sinθ and cos⁡θ\cos \thetacosθ.

[2]
b.

Starting with the identity for cos⁡(A+B)\cos(A + B)cos(A+B), find an expression for cos⁡2θ \cos 2\theta\,cos2θ in terms of sin⁡θ \sin \theta\,sinθ and cos⁡θ\cos \thetacosθ.

[2]
ci.

Use the result from part (b) to express cos⁡2θ \cos 2\theta\,cos2θ as a function of cos⁡θ \cos \theta\,cosθ only.

[2]
cii.

Use the result from part (b) to express cos⁡2θ \cos 2\theta\,cos2θ as a function of sin⁡θ \sin \theta\,sinθ only.

[2]
d.

Derive the formula for tan⁡2θ \tan 2\theta\,tan2θ in terms of tan⁡θ \tan \theta\,tanθ using the expansion of tan⁡(A+B)\tan(A + B)tan(A+B).

[2]
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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