SOLUTION: Find the value of {{{sum(cos(pi(k-5)/20), k = 0, 20)/sum(sin((k*pi)/20), k = 0, 20)}}}.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the value of {{{sum(cos(pi(k-5)/20), k = 0, 20)/sum(sin((k*pi)/20), k = 0, 20)}}}.      Log On


   

Question 457926: Find the value of .
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We can use the sum/difference formulas for cosine to simplify the expression to



Note that the expression is equal to zero, because if you were to draw all the angles on a unit circle, you would see that there are corresponding pairs of angles that add up to zero, since cos x = -cos (pi - x). The denominator of the fraction is some positive number because the sine of each angle is either positive or zero. Therefore the entire expression is equal to .