Consider the five angles _k= 5 + 2k 5

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Consider the five angles θk=π5+2kπ5,k=0,1,2,3,4.\theta_k=\frac{\pi}{5}+\frac{2k\pi}{5},\quad k=0,1,2,3,4. (a) Express each θk\theta_k as an equivalent angle lying in the interval [0,2π)[0,2\pi). (b) Hence, or otherwise, show that sin⁡θ0+sin⁡θ1+sin⁡θ2+sin⁡θ3+sin⁡θ4=0.\sin\theta_0+\sin\theta_1+\sin\theta_2+\sin\theta_3+\sin\theta_4=0. Give full reasoning in your proof.

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