怎样求sin27°的准确值准确值,不是小数,是有根号的,

Question

怎样求sin27°的准确值
准确值,不是小数,是有根号的,

Answer 1

这个嘛.
sin2*18°=cos3*18°
2cos18sin18=4(cos18)^3-3cos18
2sin18=4(cos18)^2-3
4(sin18)^2+2sin18-1=0
sin18=(√5-1)/4
cos18=[√(10+2√5)]/4=2(cos9)^2-1
得cos9=√{1+√(10+2√5)]/4/2}
cos27=4(cos9)^3-3cos9=4[√{1+√(10+2√5)]/4/2}]^3-3√{1+√(10+2√5)]/4/2}
sin27=√[1-(4[√{1+√(10+2√5)]/4/2}]^3-3√{1+√(10+2√5)]/4/2})^2]