Hello. Sorry to be a nuisance to you guys but you've all been very helpful. This is going to be my last question.
sin(3pi / 10) = (1 + squareroot 5) / 4
Find the exact value of cos(pi / 5)
This is the second part of a question. The first part mentioned something about sin(2pi / t) = cos t so I guess I have to somehow incorporate this identity. You don't have to solve it (although you could if you want to) but it would be great if you could provide me a starting point so I could work my way through. I was thinking that perhaps a unit circle diagram may help.
Thankyou very much. Of course, all help is appreciated. (happy)
Direction to solution:
Firstly, look at the roots of the equation z^5 + 1 = 0, where z is a complex number. This equation has 5 complex roots, where /z/=1 and arg(z) = (pi/5) + k*2(pi/5), with k element of .
The equation can be written in two fashions:
2) (z-1)*(z^4 - z^3 + z^2 - z+1) = 0
These equations should be identical i.e. the coefficients are the same. This will yield two equations with cos(pi/5) and cos(3pi/5) the two unknowns.