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⁡(θ−α)R\cos(\theta - \alpha) for acos⁡θ+bsin⁡θa\cos\theta + b\sin\theta?

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

For acos⁡θ+bsin⁡θ=Rcos⁡(θ−α)a\cos\theta + b\sin\theta = R\cos(\theta - \alpha), what is tan⁡α\tan\alpha?

tan⁡α=ba\tan\alpha = \frac{b}{a}

For acos⁡θ+bsin⁡θ=Rsin⁡(θ+α)a\cos\theta + b\sin\theta = R\sin(\theta + \alpha), what is tan⁡α\tan\alpha?

tan⁡α=ab\tan\alpha = \frac{a}{b}

What is RR for 3cos⁡θ+4sin⁡θ3\cos\theta + 4\sin\theta?

R=5R = 5

In the derivation, what does aa equal?

a=Rcos⁡αa = R\cos\alpha

For 3cos⁡θ+4sin⁡θ3\cos\theta + 4\sin\theta, what is tan⁡α\tan\alpha when expressing as Rcos⁡(θ−α)R\cos(\theta - \alpha)?

tan⁡α=43\tan\alpha = \frac{4}{3}

If 5cos⁡(θ−α)=25\cos(\theta - \alpha) = 2, what is cos⁡(θ−α)\cos(\theta - \alpha)?

cos⁡(θ−α)=25\cos(\theta - \alpha) = \frac{2}{5}

R addition formulae are useful for which application?

Solving trigonometric equations

What expands to Rcos⁡αcos⁡θ+Rsin⁡αsin⁡θR\cos\alpha\cos\theta + R\sin\alpha\sin\theta?

Rcos⁡(θ−α)R\cos(\theta - \alpha)

In AC circuits, what do R addition formulae analyse?

Sinusoidal voltages out of phase

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