Expert: Sherman D. - 3/28/2008

Question
This is what the exact question states:

EG: cos 36 = (sqrt5 + 1)/4
You have also been provided with the sum and difference formulas and the sin2x and cos2x formulas. Use this information to express sinx, where x is an integer between 0 to 90. Express them in terms of rational numbers and radicals for as many values as possible.

Express specific values of x please.

Answer
if you are asking me to find sin(x), and not how to find out how they got cos(36) to be (sqrt(5) + 1)/4, then

cos(36) = (sqrt(5) + 1)/4

(sqrt(5) + 1)^2 + y^2 = 4^2
((sqrt(5) + 1)(sqrt(5) + 1)) + y^2 = 16
(5 + sqrt(5) + sqrt(5) + 1) + y^2 = 16
2sqrt(5) + 6 + y^2 = 16
y^2 = 10 - 2sqrt(5)
y = sqrt(10 - 2sqrt(5))

sin(36) = sqrt(10 - 2sqrt(5))/4 or sqrt(2(5 - sqrt(5)))/4