参数方程x=t+sint,y=2+cost在t=π/4的切线

题目

参数方程x=t+sint,y=2+cost在t=π/4的切线

答案

x(π/4)=π/4+√2/2
y(π/4)=2+√2/2
x'(t)=1+cost,
y'(t)=-sint
当π/4时,切线斜率k=y'(t)/x'(t)=(1+√2/2)/(-√2/2)=-(1+√2)
由点斜式得切线方程为：y=-(1+√2)(x-π/4-√2/2)+2+√2/2