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3.5 Trigonometry (A-level only)

3.5 Trigonometry (A-level only)

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Question 15

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

In a study of harmonic oscillations, the phase angle ϕ\phiϕ (in degrees) of a combined wave satisfies the equation

3sin⁡(ϕ+45∘)=2cos⁡(ϕ−60∘) 3 \sin(\phi + 45^\circ) = 2 \cos(\phi - 60^\circ) 3sin(ϕ+45∘)=2cos(ϕ−60∘)
a.

Show that

tan⁡ϕ=2−33−6 \tan \phi = \frac{\sqrt{2} - 3}{3 - \sqrt{6}} tanϕ=3−6​2​−3​
[5]
b.

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

3sin⁡(3θ+45∘)=2cos⁡(3θ−60∘) 3 \sin(3\theta + 45^\circ) = 2 \cos(3\theta - 60^\circ) 3sin(3θ+45∘)=2cos(3θ−60∘)

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)

225 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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