SOLUTION: Please help Given that the exact value of cos pi/5 = 1 + sqrt5/4, for each question calculate the exact value of the given expression. You may leave nested radicals in your answe

Algebra ->  Trigonometry-basics -> SOLUTION: Please help Given that the exact value of cos pi/5 = 1 + sqrt5/4, for each question calculate the exact value of the given expression. You may leave nested radicals in your answe      Log On


   

Question 1115507: Please help
Given that the exact value of cos pi/5 = 1 + sqrt5/4, for each question calculate the exact value of the given expression. You may leave nested radicals in your answer.
18. Cos 2pi/5
19. Cos pi/10
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Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we are given cos pi/5 = 1 + sqrt5/4
:
18. cos (2pi/5) = ?
:
use the double angle identity
:
cos(2x) = 2 * cos^2 (x) - 1
:
cos (2pi/5) = 2 * (1 + sqrt(5/4))^2 - 1 =
:
2 * (1 + 2 * sqrt(5/4) + 1.25) - 1 =
:
2 + 4 * sqrt(5/4) + 2.50 - 1 =
:
3.50 + 4 * sqrt(5/4) =
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3.50 + 2 * sqrt(5)
:
Note sqrt(5/4) = sqrt(5)/2
:
19. Cos pi/10 = ?
:
use the half angle identity
:
cos(x/2) = sqrt((1+cos(x))/2)
:
cos(pi/10) = sqrt((1+1+sqrt(5/4))/2) =
:
sqrt((2+sqrt(5/4))/2) =
:
sqrt(4 + sqrt(5))/2
: