向量,空间直线参数方程x^2+y^2=25,z=1/∏arctan(x/y)求空间直线的参数方程,即x=x(t),y=y(t),z=z(t)Z=(1/pi)arctan(x/y)-----------------------------------------x=5sin(t),y=5cos(t),这2个怎么得到的

Question

向量,空间直线参数方程
x^2+y^2=25,
z=1/∏arctan(x/y)
求空间直线的参数方程,即x=x(t),y=y(t),z=z(t)
Z=(1/pi)arctan(x/y)
-----------------------------------------
x=5sin(t),
y=5cos(t),
这2个怎么得到的

Answer 1

z=arctan(x/y)/π
x/y=tan(πz),
x=5sin(t),
y=5cos(t),
x/y=tant,
tant=tan(πz).
z=t/π,
故参数方程为:
x=5sint,
y=5cost,
z=t/π.