R addition formulae Rcos Rsin etc (AQA A-Level Mathematics): Quizzes

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R addition formulae Rcos Rsin etc
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What is the value of RR in the expression Rcos(θα)R\cos(\theta - \alpha) for acosθ+bsinθa\cos\theta + b\sin\theta?

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

For acosθ+bsinθ=Rcos(θα)a\cos\theta + b\sin\theta = R\cos(\theta - \alpha), what is tanα\tan\alpha?

tanα=ba\tan\alpha = \frac{b}{a}

For acosθ+bsinθ=Rsin(θ+α)a\cos\theta + b\sin\theta = R\sin(\theta + \alpha), what is tanα\tan\alpha?

tanα=ab\tan\alpha = \frac{a}{b}

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

R=5R = 5

In the derivation, what does aa equal?

a=Rcosαa = R\cos\alpha

For 3cosθ+4sinθ3\cos\theta + 4\sin\theta, what is tanα\tan\alpha when expressing as Rcos(θα)R\cos(\theta - \alpha)?

tanα=43\tan\alpha = \frac{4}{3}

If 5cos(θα)=25\cos(\theta - \alpha) = 2, what is cos(θα)\cos(\theta - \alpha)?

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

R addition formulae are useful for which application?

Solving trigonometric equations

What expands to Rcosαcosθ+RsinαsinθR\cos\alpha\cos\theta + R\sin\alpha\sin\theta?

Rcos(θα)R\cos(\theta - \alpha)

In AC circuits, what do R addition formulae analyse?

Sinusoidal voltages out of phase

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