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

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