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

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R addition formulae Rcos Rsin etc
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What is RR equal to in the R addition formulae for acosθ+bsinθa\cos\theta + b\sin\theta?

R=a2+b2R = \sqrt{a^2 + b^2}

For Rcos(θα)R\cos(\theta - \alpha) form, what is tanα\tan\alpha equal to?

tanα=ba\tan\alpha = \frac{b}{a}

For Rsin(θ+α)R\sin(\theta + \alpha) form, what is tanα\tan\alpha equal to?

tanα=ab\tan\alpha = \frac{a}{b}

What is the value of RR for 3cosθ+4sinθ3\cos\theta + 4\sin\theta?

R=5R = 5

What is 3cosθ+4sinθ3\cos\theta + 4\sin\theta equal to in Rcos(θα)R\cos(\theta - \alpha) form?

5cos(θα)5\cos(\theta - \alpha)

After converting 3cosθ+4sinθ=23\cos\theta + 4\sin\theta = 2 to 5cos(θα)=25\cos(\theta - \alpha) = 2, what's next?

cos(θα)=25\cos(\theta - \alpha) = \frac{2}{5}

What is a key use of R addition formulae?

Solving trigonometric equations

In which field are R addition formulae used to analyse AC circuits?

Electrical engineering

What does aa equal in the derivation when comparing to Rcos(θα)R\cos(\theta - \alpha)?

a=Rcosαa = R\cos\alpha

Which application involves oscillations and wave motion in physics?

Oscillatory motion

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