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Let A1 A2 A3 A4 A5 A6 A1 be a regular he...

Let `A_1 A_2 A_3 A_4 A_5 A_6 A_1` be a regular hexagon. Write the x-components of the vectors representeed by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that `cos0+cospi/3+cos(2pi)/3+cos(4pi)/3+cos(5pi)/3=0` Use the known cosine values of verify the result.
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