Skip to content

Course home

Trigonometry

Trigonometry

Medium
1234
Question 4
a(i).

By writing 3θ=(2θ+θ)3\theta = (2\theta + \theta)3θ=(2θ+θ), show that

sin⁡3θ=3sin⁡θ−4sin⁡3θ. \sin 3\theta = 3 \sin \theta - 4 \sin^3 \theta. sin3θ=3sinθ−4sin3θ.
[4]
a(ii).

Hence, or otherwise, for 0<θ<π3\displaystyle 0 < \theta < \frac{\pi}{3}0<θ<3π​, solve

8sin⁡3θ−6sin⁡θ+1=0. 8 \sin^3 \theta - 6 \sin \theta + 1 = 0. 8sin3θ−6sinθ+1=0.

Give your answers in terms of π\piπ.

[5]
b.

Using sin⁡(θ−α)=sin⁡θcos⁡α−cos⁡θsin⁡α\sin(\theta - \alpha) = \sin \theta \cos \alpha - \cos \theta \sin \alphasin(θ−α)=sinθcosα−cosθsinα, or otherwise, show that

sin⁡15∘=14(6−2). \sin 15^\circ = \frac{1}{4}(\sqrt{6} - \sqrt{2}). sin15∘=41​(6​−2​).
[4]
Markscheme

Trigonometry Questions

  1. A Level
  2. /Old Maths
  3. /Trigonometry

4 exam-style questions on Edexcel A Level Old Maths Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank