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求解答,急,谢谢
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首先,t=0时x=0,y=1
由题意,dx/dt=e^tcost+sinte^t
dy/dt=-e^tsint+coste^t
dy/dx=(dy/dt)/(dx/dt)
=(-e^tsint+coste^t)/(e^tcost+sinte^t)
=(cost-sint)/(cost+sint)
=(cost-sint)(cost+sint)/(cost+sint)^2
=((cost)^2-(sint)^2)/(sint)^2+(cost)^2+2sintcost
=cos2t/1+sin2t
因为t=0,所以此处斜率=1
切线方程: y=x+1
由题意,dx/dt=e^tcost+sinte^t
dy/dt=-e^tsint+coste^t
dy/dx=(dy/dt)/(dx/dt)
=(-e^tsint+coste^t)/(e^tcost+sinte^t)
=(cost-sint)/(cost+sint)
=(cost-sint)(cost+sint)/(cost+sint)^2
=((cost)^2-(sint)^2)/(sint)^2+(cost)^2+2sintcost
=cos2t/1+sin2t
因为t=0,所以此处斜率=1
切线方程: y=x+1
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