设（X=TCOST,Y=TSINT,求DY/DX

题目

设（X=TCOST,Y=TSINT,求DY/DX

答案

先求dx=(cost-tsint)dt,dy=(sint+tcost)dt
然后dy/dx=(sint+tcost)/(cost-tsint)
根据x=tcost ; y=tsint; y/x=tant
所以dy/dx=[y+yarctan(y/x)]/[x-yarctan(y/x)]