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Math Help - Expression for sin(1 degree)?

  1. #1
    Senior Member TriKri's Avatar
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    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?
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    Quote Originally Posted by TriKri View Post
    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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