【证明】三角函数都是代数数

风花飘飘

sin(40°)= (%i/16-sqrt(3)/16)^(1/3)+1/(4*(%i/16-sqrt(3)/16)^(1/3))

= ((%i-sqrt(3))^(2/3)+2^(2/3))/(2^(4/3)*(%i-sqrt(3))^(1/3))

风花飘飘

叙述符号 i
=(((%i-sqrt(3))^(2/3)+2^(2/3))/(2^(4/3)*(%i-sqrt(3))^(1/3)))*(2*(-1)^(40/180)/(1-(-1)^(40/90)))