Question

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
x = t cos t, y = t sin t; t = π

Answer 1

dx/dt=-tsint+cost , dy/dt=tcost+sint
Plug pi = ( pi x cos(pi) + sin(pi) ) / -(pi) x sin(pi) + cos(pi) = ( 1(-1) + 0 ) / (-1(0) + 1 = -1/1 = -1 = slope

Answer 2

Now to find (x,y).
y = (pi) x sin(pi) = pi x 0 = 0
x = (pi) x cos(pi) = pi x (-1) = -pi
(x,y) = (-pi, 0)

Equation of tangent: y-0 = -1 (x-(-pi)
y - 0 = -x - pi
y = - x - pi [answer]