Compound & Double Angle Formulae (AQA 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)

Which is NOT a form of cos⁡(2θ)\cos(2\theta)?

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

What is tan⁡(2θ)\tan(2\theta) equal to?

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) using 2cos⁡2(θ)−12\cos^2(\theta) - 1?

−119169\frac{-119}{169}

For tan⁡(2θ)=1\tan(2\theta) = 1 in 0∘≤θ≤180∘0^\circ \leq \theta \leq 180^\circ, what are the solutions?

22.5∘22.5^\circ and 112.5∘112.5^\circ

When solving cos⁡(2x)+cos⁡x=0\cos(2x) + \cos x = 0, which form gives x=60∘,180∘,300∘x = 60^\circ, 180^\circ, 300^\circ?

cos⁡(2x)=2cos⁡2x−1\cos(2x) = 2\cos^2 x - 1

Why is dividing by cos⁡x\cos x a bad method when solving sin⁡2x+cos⁡x=0\sin 2x + \cos x = 0?

You lose solutions where cos⁡x=0\cos x = 0

Double angle formulae are derived from which identities?

Compound angle formulae by setting A=BA = B

Solving sin⁡2x+cos⁡x=0\sin 2x + \cos x = 0 for 0≤x≤2π0 \leq x \leq 2\pi by factorising gives which solutions?

π2,7π6,3π2,11π6\frac{\pi}{2}, \frac{7\pi}{6}, \frac{3\pi}{2}, \frac{11\pi}{6}

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