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)1tan2(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 2cos2(θ)12\cos^2(\theta) - 1?

119169\frac{-119}{169}

For tan(2θ)=1\tan(2\theta) = 1 in 0θ1800^\circ \leq \theta \leq 180^\circ, what are the solutions?

22.522.5^\circ and 112.5112.5^\circ

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

cos(2x)=2cos2x1\cos(2x) = 2\cos^2 x - 1

Why is dividing by cosx\cos x a bad method when solving sin2x+cosx=0\sin 2x + \cos x = 0?

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

Double angle formulae are derived from which identities?

Compound angle formulae by setting A=BA = B

Solving sin2x+cosx=0\sin 2x + \cos x = 0 for 0x2π0 \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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