Trygonometria, zadanie nr 4500
ostatnie wiadomości | regulamin | latex
Autor | Zadanie / Rozwiązanie |
petrus postów: 64 | 2014-09-07 14:58:26 Da ktoś radę to skrócić, albo wie jaki program to wykona? Jest tu mowa o trójkącie, stąd między kątami i długościami też można znaleźć jakieś zależności. Każdy program jaki sprawdzałem się poddał, więc nie wiem czy czeka mnie 100 stron obliczeń czy może da się to uprościć "bezboleśnie" $((sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))*cos(\beta)- (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))sin(\beta))*sqrt(1-(((sqrt(b*b+a*a/4-a*b*cos(\gamma)))*((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma))))/( ((sqrt(b*b+a*a/4-a*b*cos(\gamma)))*sqrt(1+(((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma)))* ((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma))))/(c*c)-2*(sqrt(1-(sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))* (sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))))* ((b*c*sin(beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma)))/c))*c)* (sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))))* (((sqrt(b*b+a*a/4-a*b*cos(\gamma)))*((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma))))/( ((sqrt(b*b+a*a/4-a*b*cos(\gamma)))*sqrt(1+(((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma)))* ((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma))))/(c*c)-2*(sqrt(1-(sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))* (sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))))* ((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma)))/c))*c)* (sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))))+( (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))cos(\beta)+sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))*sin(\beta))* (((sqrt(b*b+a*a/4-a*b*cos(\gamma)))*((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma))))/( ((sqrt(b*b+a*a/4-a*b*cos(\gamma)))*sqrt(1+(((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma)))* ((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma))))/(c*c)-2*(sqrt(1-(sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))* (sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))))))* ((b*c*sin(\beta)-a*c*sin(\gamma))/(c*sin(\alpha)-a*sin(\gamma)))/c))*c)* (sin(\alpha)*(1-2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))-cos(\alpha)*2*(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))*sqrt(1-(sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma)))))* (sin(\gamma)*a/(2*(sqrt(b*b+a*a/4-a*b*cos(\gamma))))))))$ |
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