*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?

-1/2 radian?

BTW, I am taking a course in calculus, on DVD's (4 of them) by 'the teaching company'. The prof is Michael Starbird Phd, and I really wished I had a teacher that good when I was in college, this guy is incredible, with new results from recent mathemeticians and excellent visuals and step by step explainations of the concepts behind like derivitives and integrals and such, overall, a GREAT course, highly recommended. If you take that course before you get to college you will be well on your way to an A in calculus!

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.