一度の三角関数の解析値
「一度の三角関数にむけて - notes plastiques」の続き。
maximaを使うことで計算できた。
cos1:-sqrt(-2^(4/3)*(4^(1/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)*sqrt(-2*4^(11/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(2/3)+2^(13/2)*sqrt(3-sqrt(5))*%i*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(13/2)*sqrt(sqrt(5)+5)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+4^(13/3))+32*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(7/2)*4^(1/3)*sqrt(3-sqrt(5))*%i+2^(7/2)*4^(1/3)*sqrt(sqrt(5)+5))^(1/3)-4^(22/9)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(4/9)/(4^(1/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)*sqrt(-2*4^(11/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(2/3)+2^(13/2)*sqrt(3-sqrt(5))*%i*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(13/2)*sqrt(sqrt(5)+5)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+4^(13/3))+32*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(7/2)*4^(1/3)*sqrt(3-sqrt(5))*%i+2^(7/2)*4^(1/3)*sqrt(sqrt(5)+5))^(1/3)+2^(5/3)*4^(11/9)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(2/9))/(2^(13/9)*4^(5/9)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/9)); sin1:-sqrt(-2^(4/3)*(4^(1/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)*sqrt(-2*4^(11/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(2/3)+2^(13/2)*sqrt(3-sqrt(5))*%i*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(13/2)*sqrt(sqrt(5)+5)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+4^(13/3))+32*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(7/2)*4^(1/3)*sqrt(3-sqrt(5))*%i+2^(7/2)*4^(1/3)*sqrt(sqrt(5)+5))^(1/3)-4^(22/9)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(4/9)/(4^(1/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)*sqrt(-2*4^(11/3)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(2/3)+2^(13/2)*sqrt(3-sqrt(5))*%i*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(13/2)*sqrt(sqrt(5)+5)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+4^(13/3))+32*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/3)+2^(7/2)*4^(1/3)*sqrt(3-sqrt(5))*%i+2^(7/2)*4^(1/3)*sqrt(sqrt(5)+5))^(1/3)+2^(5/3)*4^(11/9)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(2/9))/(2^(13/9)*4^(5/9)*(sqrt(2)*sqrt(3-sqrt(5))*%i+sqrt(2)*sqrt(sqrt(5)+5))^(1/9));
maximaはmacportsやapt-getなどで入れられる。
maximaに入力した命令はこちら
