Originally posted by kbaumen
I had this as homework in my algebra course and it took a fair amount of time for me to find the solution. It's actually quite difficult to notice.
Prove the identity:
cos(2pi/7) + cos(4pi/7) + cos(6pi/7) = -1/2
Well for a reality check, I did the calcs on my casio and finally convinced myself, any one of those worked out = 0.999 something and added together, it =2.999 or so. Don't see how that works out to be minus 1/2.
Even if it was supposed to be inverted it would come out to 1/3 or so, a far cry from 1/2.
Are the units in degrees? or maybe radians?
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Back to the cosign: 2Pi is 6.28 and /7= 0.897 and cos (0.8970) = 0.999 any way you look at it and making it 2PI or 4PI or 6PI doesn't change it much, only in the 4th and 5th digit, so can't see adding those three values and coming up with anything like 1/2 or -1/2.