Hogyan számolom ki az x=t−sin (t), y=1−cos (t) paraméteresen adott síkgörbe t_0=3 -beli érintőjének egyenletét?

dx/dt = 1 - cos(t)

dy/dt = sin(t)

t=3 esetén

x(3) = 3-sin(3)

y(3) = 1-cos(3)

dx/dt (3) = 1-cos(3)

dy/dt = sin(3)

Az egyenlet:

y-1+cos(3) = sin(3)/(1-cos(3)) * (x-3+sin(3))

y=[sin(3)/(1-cos(3))]x + sin²(3)/(1-cos(3)) +1-cos(3) +3sin(3)/(cos(3)-1)

y=[sin(3)/(1-cos(3))]x + 2(1-cos(3))/(1-cos(3)) - 3sin(3)/(1-cos(3))

y = [sin(3)/(1-cos(3))]x + 2 -3sin(3)/(1-cos(3))