Double Angle Formulae (Edexcel A-Level Mathematics): Quizzes

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Double Angle Formulae
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What is the double angle formula for sin⁡(2θ)\sin(2\theta)?

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

How many equivalent forms exist for cos⁡(2θ)\cos(2\theta)?

Three

What is the double angle formula for tan⁡(2θ)\tan(2\theta)?

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

If sin⁡(θ)=35\sin(\theta) = \frac{3}{5} and cos⁡(θ)=45\cos(\theta) = \frac{4}{5}, what is sin⁡(2θ)\sin(2\theta)?

2425\frac{24}{25}

If cos⁡(θ)=513\cos(\theta) = \frac{5}{13}, what is cos⁡(2θ)\cos(2\theta)?

−119169\frac{-119}{169}

For 0°≤θ≤180°0° \leq \theta \leq 180°, solve tan⁡(2θ)=1\tan(2\theta) = 1.

22.5°,112.5°22.5°, 112.5°

Which form of cos⁡(2θ)\cos(2\theta) is most useful when simplifying in terms of sin⁡(θ)\sin(\theta)?

1−2sin⁡2(θ)1 - 2\sin^2(\theta)

How are double angle formulae derived?

From compound angle formulae by setting A=BA = B

When solving sin⁡2x+cos⁡x=0\sin 2x + \cos x = 0, why factorize rather than divide by cos⁡x\cos x?

To avoid losing solutions where cos⁡x=0\cos x = 0

Which is NOT an application of double angle formulae?

Finding exact values of logarithms

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