7

Is there a known Generalized algebraic formula for the following:

$\sin(\pi/n)$

here, $n$ is an positive integer

user1729
  • 31,015
GSA_1
  • 187
  • 2
    You can get various infinite families of these values by starting with a known one of them and repeatedly applying a half-angle formula. – coffeemath Mar 25 '21 at 19:53
  • Good question, I think you should put it as $\sin(\frac{2\pi}{n})$ instead, $n \in \mathbb{Z}$ – Aderinsola Joshua Mar 25 '21 at 19:55
  • 2
    $\sin\frac\pi n$ is a very nice and a very general formula. – user Mar 25 '21 at 19:59
  • 4
    $\cos n\theta+i\sin n\theta=(\cos \theta+i\sin \theta)^n$ together with binomial expansion gives you multiple angle formulas for $\cos n\theta$ and $\sin n\theta.$ But (as far as I know) there is no algebraic formula for $\sin(\theta/n)$ in terms of $\sin \theta, \cos\theta.$ – Bumblebee Mar 25 '21 at 20:01
  • 1
    Also see https://en.wikipedia.org/wiki/Chebyshev_polynomials – Kenta S Mar 25 '21 at 21:12

0 Answers0