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3.4.7 Trigonometry (A-level only)

3.4.7 Trigonometry (A-level only)

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Question 11
i.

Show that

cot⁡θ−tan⁡θcot⁡θ+tan⁡θ≡cos⁡2θ \frac{\cot \theta - \tan \theta}{\cot \theta + \tan \theta} \equiv \cos 2\theta cotθ+tanθcotθ−tanθ​≡cos2θ

for θ≠nπ2\theta \neq \frac{n\pi}{2}θ=2nπ​ where n∈Zn \in \mathbb{Z}n∈Z.

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ii.

The power output PPP (in Watts) of a specific AC circuit component is modelled by the function P(t)=11cos⁡2(2t−40∘)P(t) = 11 \cos^2(2t - 40^\circ)P(t)=11cos2(2t−40∘), where ttt is a phase angle measured in degrees and 0∘≤t<90∘0^\circ \le t < 90^\circ0∘≤t<90∘.

Determine the values of ttt for which the power output is exactly 333 Watts, giving your answers to one decimal place. (Solutions based entirely on graphical or numerical methods are not acceptable.)

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Markscheme

3.4.7 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.4.7 Trigonometry (A-level only)

38 exam-style questions on CCEA A Level Maths 3.4.7 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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