Solve the following trigonometric equation for in the interval .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve the following trigonometric equation for θ\theta in the interval 0≤θ<2π0 \le \theta < 2\pi. (i) Show that cos⁡2θ=12\cos 2\theta = \dfrac12 implies 2θ=2nπ±π3,  n∈Z2\theta = 2n\pi \pm \dfrac{\pi}{3},\; n \in \mathbb Z. (ii) Hence list all values of θ\theta in the interval 0≤θ<2π0 \le \theta < 2\pi that satisfy the given equation.

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