解一方程已知X=Vt-Rsin(Vt/R)Y=R-Rcos(Vt/R)X,Y,R,V为已知量求t用反三角函数时请详悉一点

Question

解一方程
已知 X=Vt-Rsin(Vt/R)
Y=R-Rcos(Vt/R) X,Y,R,V为已知量 求t
用反三角函数时请详悉一点

Answer 1

X=Vt-Rsin(Vt/R)
Y=R-Rcos(Vt/R)
Rsin(Vt/R)=Vt-X
Rcos(Vt/R)=R-Y
(Rsin(Vt/R))^2=(Vt-X)^2
(Rcos(Vt/R))^2=(R-Y)^2
(Rsin(Vt/R))^2+(Rcos(Vt/R))^2=(Vt-X)^2+(R-Y)^2
R^2*(sin(Vt/R))^2+(cos(Vt/R))^2)=(Vt-X)^2+(R-Y)^2
R^2=(Vt-X)^2+(R-Y)^2
(Vt-X)^2=R^2-(R-Y)^2
Vt-X=(R^2-(R-Y)^2)^0.5
Vt=(R^2-(R-Y)^2)^0.5+X
Vt=((R+R-Y)*(R-R+Y)))^0.5+X
=(2*R*Y-Y^2)^0.5+X
t=((2*R*Y-Y^2)^0.5+X)/V