x=2acost-acos2t y=2asint-asin2t 求t为几时这个曲线有垂直或水平切线,

x=2acost-acos2t,
y=2asint-asin2t,
x'=-2asint+2asin2t,
y'=2acost-2acos2t,
由x'=0得sint=sin2t=2sintcost,
∴sint=0,或cost=1/2,
∴t=kπ或(2k土1/3)π,k∈Z,此时曲线有垂直切线.
由y'=0得cost-cos2t=0,2(cost)^2-cost-1=0,
解得cost=1或-1/2,
∴t=2kπ,或(2k土2/3)π,此时曲线有水平切线.
2.t=π/4时x=a√2,y=a(√2-1),
x'=a(2-√2),y'=a√2,dy/dx=y'/x'=√2+1,
其切线方程是y-a(√2-1）=(√2+1)(x-a√2),
即y=(√2+1)x-3.
3.仿2,留给您练习.