Double Angle Formulae (AQA A-Level Mathematics): Flashcards

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Double Angle Formulae
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sin⁡(2θ)\sin(2\theta) formula

2sin⁡(θ)cos⁡(θ)2\sin(\theta)\cos(\theta)

cos⁡(2θ)\cos(2\theta) in terms of sin⁡2\sin^2 and cos⁡2\cos^2

cos⁡2(θ)−sin⁡2(θ)\cos^2(\theta) - \sin^2(\theta)

cos⁡(2θ)\cos(2\theta) in terms of cos⁡\cos only

2cos⁡2(θ)−12\cos^2(\theta) - 1

cos⁡(2θ)\cos(2\theta) in terms of sin⁡\sin only

1−2sin⁡2(θ)1 - 2\sin^2(\theta)

Number of equivalent forms for cos⁡(2θ)\cos(2\theta)

Three

tan⁡(2θ)\tan(2\theta) formula

2tan⁡(θ)1−tan⁡2(θ)\frac{2\tan(\theta)}{1 - \tan^2(\theta)}

What double angle formulae express

Trig functions of 2θ2\theta in terms of θ\theta

Double angle formulae use in calculus

Simplify integrals/derivatives with trig functions

Physics uses of double angle formulae

Wave mechanics, signal processing, oscillations

Why factor rather than divide in trig equations

To avoid losing solutions

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