求大神解一下这道题目

2025-03-22 22:12:34
推荐回答(2个)
回答1:


标准答案

回答2:

dx/dt=1-cost
dy/dt=sint
所以对P(x,y)处切线的切线斜率=dy/dx
=sint/(1-cost)
=2cos(t/2)sin(t/2)/2sin^2(t/2)
=cot(t/2)
因为该切线与x轴倾角为a,所以tana=cot(t/2)
a=π/2-t/2
cosa/√y=cos(π/2-t/2)/√(1-cost)
=sin(t/2)/√[2sin^2(t/2)]
=√2/2