Question

How do you evaluate `sin(pi/7)`?

Answer 1

`sin(pi/7)~~0.4338837391`

Explanation:

If the question real is HOW to do this evaluation:

[1] For all practical purposes, use a calculator (or spreadsheet function).

[2] I you must to this mechanically, you could use the series:
`color(white)("XXX")sin(x) =Sigma_(n=0)^L (-1)^n 1/((2n+1)!)*x^(2n+1)`
with a significantly large value of `L` so that successive terms are very small. In this case using `3.14159` for `pi`, my results did not improve significantly beyond `L=4` and were less than `0.001%` away from the true value for `sin(pi/7)`