Talk:Trigonometry/The sine of 18 degrees

It would be possible to add another page giving the sines and cosines of 3º, 6º etc. This can be done by solving the quintics arising from sin(5x) equal to various other numbers or by using the half angle formula to get the sine and cosine of 15º and then use sin(a+b) and related formulae. Would this have much educational value in the context of trigonometry or would it just be a jungle of surds?--Wisden (discuss • contribs) 11:20, 4 April 2011 (UTC)

Well, you could, but I don't think that people would find it very interesting or enlightening. I managed to find the sine of 3º before, and it wasn't fun. I didn't end up learning anything, either. I would just stick with the sine of 18º. --Oneequalstwo (discuss • contribs) 05:25, 26 December 2011 (UTC)

Actually, I was thinking of adding a purely geometric way of finding the sine of 18º - take a 36º-72º-72º isosceles triangle with a base of length 1, bisect the 72º angle, and then using similar triangles to solve for the legs of the triangle. You can then use the height of the triangle to find sin(18º). I could do this once I learn how to format things on this Wiki, if people think that this is a good idea. I can also make a diagram to go with the explanation. --Oneequalstwo (discuss • contribs) 05:25, 26 December 2011 (UTC)

Solving equation of degree 5
I have removed the last remark of solving sine of any angle x/5 when sine of x is known, since it must involve solving a fifth degree equation, which is generally not feasible. 160.39.84.81 (discuss) 15:45, 22 August 2013 (UTC)