Let A1A2A3A4A5A6A1 be regular hexagon. Write the x-components of the v

1.	Let A1A2A3A4A5A6A1 be regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that cos 0+cos π3+cos 2π3+cos 3π3+cos 4π3+cos 5π3=0. Use the known cosine values to verify the result.
Answer» Let $A_{1} A_{2} A_{3} A_{4} A_{5} A_{6} A_{1}$ be regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that $c o s 0 + c o s \frac{π}{3} + c o s \frac{2 π}{3} + c o s \frac{3 π}{3} + c o s \frac{4 π}{3} + c o s \frac{5 π}{3} = 0$ . Use the known cosine values to verify the result.

Let A1A2A3A4A5A6A1 be regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that cos 0+cos π3+cos 2π3+cos 3π3+cos 4π3+cos 5π3=0. Use the known cosine values to verify the result.

Answer»

Let $A_{1} A_{2} A_{3} A_{4} A_{5} A_{6} A_{1}$ be regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact that the resultant of these six vectors is zero, to prove that $c o s 0 + c o s \frac{π}{3} + c o s \frac{2 π}{3} + c o s \frac{3 π}{3} + c o s \frac{4 π}{3} + c o s \frac{5 π}{3} = 0$ .

Use the known cosine values to verify the result.

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