Expression for sin(1 degree)?

**TriKri** · November 30th 2006, 03:13 PM

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?

**ThePerfectHacker** · November 30th 2006, 05:48 PM

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.

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