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3.5 Trigonometry (A-level only)

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Question 8

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

a.

Two acoustic waves are superimposed such that their resulting phase angle ϕ\phiϕ satisfies the equation

6sin⁡(ϕ−60∘)=2cos⁡(ϕ+45∘) \sqrt{6} \sin(\phi - 60^\circ) = 2 \cos(\phi + 45^\circ) 6​sin(ϕ−60∘)=2cos(ϕ+45∘)

Show that

tan⁡ϕ=52+3 \tan \phi = \frac{5}{2 + \sqrt{3}} tanϕ=2+3​5​

and hence that

tan⁡ϕ=10−53 \tan \phi = 10 - 5\sqrt{3} tanϕ=10−53​
[5]
b.

Hence or otherwise, solve for 0≤θ<180∘0 \le \theta < 180^\circ0≤θ<180∘,

6sin⁡(3θ−60∘)=2cos⁡(3θ+45∘) \sqrt{6} \sin(3\theta - 60^\circ) = 2 \cos(3\theta + 45^\circ) 6​sin(3θ−60∘)=2cos(3θ+45∘)

giving your answers to one decimal place.

[4]
Markscheme

3.5 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Trigonometry (A-level only)

223 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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