I'm trying to express cos(pi/7) with radicals - that is, basic operations (addition, division, etc) and square and cube roots (or even higher roots if necessary).
I got this far:
If and , then
Although this seems a complex expression, the imaginary part of x is actually zero, so x is in fact a real number (obviously, since cos(pi/7) is real). But I can't extract the real part as a "really real" radical expression (without i, that is).
Thanks. Still a bit confused though, the page says:
Which is also what I read elsewhere (except for the typo - that last condition should be "values of n")Originally Posted by Wolfram Mathworld
But further down, it says:
From the example, I figured that , doesn't that fit the description "in terms of finite root extraction of real numbers"?In general, any trigonometric function can be expressed in radicals for arguments of the form (...)