Expression for sin(1 degree)?

• Nov 30th 2006, 04:13 PM
TriKri
Expression for sin(1 degree)?
I have heard that it is possible to derive an expression for $sin(1^\circ)$. I have tried myself, but I have only gotten to the part where I shall derive an expression for $sin(10^\circ)$ from the expression of $sin(30^\circ)$. To get $sin(30^\circ)$ I had to use complex numbers to first get an expression for $tan(30^\circ)$, but when I try to do the same thing again I get the equation $x^3-\sqrt{3}x^2-3x = -\sqrt{\frac{1}{3}}$ (where $x = tan(10^\circ)$), but I don't know how to solve that. How do I continue?
• Nov 30th 2006, 06:48 PM
ThePerfectHacker
Quote:

Originally Posted by TriKri
I have heard that it is possible to derive an expression for $sin(1^\circ)$. I have tried myself, but I have only gotten to the part where I shall derive an expression for $sin(10^\circ)$ from the expression of $sin(30^\circ)$. To get $sin(30^\circ)$ I had to use complex numbers to first get an expression for $tan(30^\circ)$, but when I try to do the same thing again I get the equation $x^3-\sqrt{3}x^2-3x = -\sqrt{\frac{1}{3}}$ (where $x = tan(10^\circ)$), but I don't know how to solve that. How do I continue?

It is not possible. I have done this myself.
I was successful to $\sin 5^o$.
But then it leads to a quintic equation, which is not solvable through premutation of radicals.